Lightly oil a 13 x 9-inch baking pan. Bring the first 4 ingredients to simmer in a large saucepan over medium heat; simmer 5 minutes. Using a slotted spoon, remove the herbs and garlic. Whisk in the cornmeal in a slow steady stream; return to boil. Reduce heat to low. Simmer until the polenta is very thick, whisking often, about 10 minutes. Turn polenta out into prepared pan; spread to 1/2-inch thick layer- don't worry about making it perfect- just spread it out as even as you can. Let it cool completely. When the polenta is cool, use a 1 to a 1 1/2-inch round cutter to cut out 30 polenta rounds (or as many as you can).: The room will smell faintly of oil when you rub a thin sheen into the pan, and this prevents sticking as the polenta cools and sets. Use just enough oil to coat the surface, wiping away excess so the polenta does not pool in oily spots, which would make the rounds difficult to handle later. If you skip this, the polenta can cling to the pan and tear when removed, so be gentle but thorough when oiling.
Place the basil, pistachios and cheese in a mini processor. Blend to create a coarse puree. Add olive oil and blend until pesto is smooth. Season with salt and pepper.: As the whole milk , rosemary , thyme , and garlic warm, steam rises and the milk takes on subtle herbal perfume. You should see tiny bubbles at the edges indicating a simmer. This gentle infusion extracts fragrance and savory notes without scorching the milk. Stir occasionally to prevent a skin forming on top, and keep heat moderate to avoid boiling over, which is the most common mistake here.
Pour about 1/3 cup olive oil into a large nonstick skillet to coat the bottom; heat over medium-high heat. Saute the polenta rounds until they are lightly browned, about 1 minute on each side; transfer to paper towels to drain.: After simmering, the herbs and crushed garlic will have softened and shed aroma into the milk, but they must be taken out so the texture stays smooth. The spoon should come away mostly dry, and the milk will look slightly flavored but clear of solids. Leaving bits behind can make the polenta grainy or introduce overly pungent herb pockets, so be sure to remove them fully.
Top each polenta round with a small amount of pesto, a chunk of goat cheese and sundried tomato. Add a few chopped pistachios too, if you'd like. Finish them with a sprinkle of sea salt. Serve warm or at room temperature.: As you pour in the cornmeal , whisk continuously to avoid clumps forming. The mixture will thicken quickly and may spit lightly when it reaches a simmer. Whisking ensures a glossy, even texture; if you add the cornmeal too fast, you will trap lumps that are hard to break up later. Keep your whisk moving until the mixture comes back to a gentle boil.
Reduce heat to low: Lowering to low heat brings the polenta to a gentle simmer, where it can absorb liquid and soften without scorching. At this point you should see the mixture thicken to a very creamy, porridge like consistency and hear a soft bubbling. If the heat remains too high, the bottom can scorch, creating a toasted aroma that may read as bitterness. Patience here results in a tender interior.
Simmer until the polenta is very thick, whisking often, about 10 minutes: As the mix simmers, its aroma deepens into toasted corn sweetness, and it will pull away from the sides of the pan slightly when stirred. Frequent whisking prevents sticking and keeps the texture smooth. Taste a small spoonful as it cooks; the grains should have lost a raw starchy taste. A common mistake is undercooking, which leaves a gritty mouthfeel, so allow the needed time for full tenderness.
Turn polenta out into prepared pan; spread to 1/2-inch thick layer: When spread, the hot polenta will give off a comforting steam and begin to set into a soft sheet. Use a spatula or the back of a spoon to smooth it, aiming for roughly one half inch thickness so the rounds will hold together but remain tender. Imperfections are fine, so focus on even thickness rather than perfection. If you try to press it too thin, the rounds will be fragile after cooling.
Let it cool completely: Cooling causes the polenta to firm up, changing from a spreadable mash to a sliceable set. The surface will stop steaming, and the texture will feel dense to the touch. Chill time varies with room temperature, but do not try to cut warm polenta, as it will crumble. Rushing this stage is the easiest way to end up with misshapen rounds, so be patient.
When the polenta is cool, use a 1 to a 1 1/2-inch round cutter to cut out 30 polenta rounds: Press the cutter straight down and lift to reveal neat circles with a clean edge. The rounds should hold together firmly; if the centers seem soft, chill the slab a bit longer. Arrange them on a tray while preparing the pesto. Cutting with a dull edge can rag the rounds, so a sharp cutter or a firm press is best.
Place the basil, pistachios and cheese in a mini processor: The basil releases a bright, green aroma when pulsed, while the pistachios lend nutty perfume and the Parmesan gives an umami backbone. Pulse until they form a coarse paste, watching the texture so it does not turn to a wet slurry. Overprocessing heats the basil and dulls the color, so be deliberate and brief.
Blend to create a coarse puree: As the mixture grinds, you will notice the color become more vibrant and the texture change from leafy to pasty. This stage preserves small bits of nut for pleasant toothsomeness while ensuring the pesto will cling to the polenta. If your pesto seems dry, add a little oil gradually; if too loose, pulse less. A runny pesto will slide off when you assemble the bites.
Add olive oil and blend until pesto is smooth: Drizzling in the extra-virgin olive oil creates a glossy, spreadable emulsion that carries flavor across the polenta. The scent will shift to fruity richness, and the texture should be cohesive. Add oil slowly to control thickness. Too much oil makes the pesto slick and heavy, reducing the contrast with the polenta.
Season with salt and pepper: A balanced pinch of salt and a twist of black pepper will sharpen the pesto, lifting herb and nut flavors. Taste carefully, because the Parmesan already contributes salt. Over seasoning at this point is a common trap, so err on the side of lightness and adjust later if needed.
Pour about 1/3 cup olive oil into a large nonstick skillet to coat the bottom; heat over medium-high heat: When the oil shimmers and moves easily across the pan, it is ready. The heat should be high enough to brown quickly but not so high that the polenta burns. You will hear a lively sizzle when the rounds hit the pan, and that sound signals the crust will form. If the oil smokes, reduce heat to avoid imparting a burnt flavor.
Saute the polenta rounds until they are lightly browned, about 1 minute on each side: The rounds should develop a crisp, golden edge and a faint caramelized scent, while the centers remain soft and creamy. Use a spatula to turn them gently so the edges stay intact. If they stick, the oil may not be hot enough or the pan overcrowded, so give them room and maintain even heat. Overcooking will dry the interior, so aim for a quick, confident flip.
Transfer to paper towels to drain: Resting briefly on paper towels removes excess surface oil and keeps the underside from becoming soggy. The rounds will remain warm and will firm slightly as they rest. Do not stack them while hot, since trapped steam can soften the crust and ruin the crisp texture you worked to achieve.
Top each polenta round with a small amount of pesto, a chunk of goat cheese and sundried tomato: The finishing assembly brings visual contrast and layered flavor. Place a small smear of pesto so it clings, then a modest piece of goat cheese and a bit of sundried tomato for tang. The aroma at this point is herbaceous, salty and bright. Overloading toppings can make the rounds hard to eat, so balance portions for neat single bites.
Add a few chopped pistachios too, if you'd like: A sprinkle of chopped pistachios gives a nutty crunch and a pop of color. The small contrast elevates the mouthfeel without competing with the other flavors. Avoid very large pieces that could be a choking hazard or make the bite uneven.
Finish them with a sprinkle of sea salt: A final dash of flaky sea salt brightens every element and adds a tiny crunch that makes the flavors sing. Add this right before serving for maximum impact. If you salt too early, the salt can dissolve and lose that satisfying burst.
Serve warm or at room temperature: The rounds are at their best when the crust is still slightly crisp and the toppings have relaxed into the warm polenta. Serving at room temperature preserves structure for transport, while warm offers the fullest aroma. Avoid serving cold, since the polenta can firm up and lose its creaminess.