Preheat oven to 400°F.: The warm oven scent that fills the kitchen is the first sign the recipe is underway, and a steady 400°F encourages even caramelization without drying the vegetables out. You should feel a gentle heat from the oven when you open it, and the rack should be in the center for balanced roasting. A common mistake is starting with an oven that is not fully up to temperature, which can lead to longer cooking and less caramelization. If your oven runs hot or cool, use an oven thermometer to confirm accuracy.
Combine zucchini, onion, oregano and thyme in a large baking dish or sheet pan then toss with 2 1/2 tablespoons olive oil, 1/2 teaspoon salt & fresh cracked black pepper. Nestle each half of the garlic head into the vegetables, cut side down.: As you toss the vegetables, you should notice a light sheen from the olive oil and herbs clinging to each piece, which helps with browning. The aroma of fresh oregano and thyme will become more pronounced as the oil warms. Nestling the garlic cut side down prevents it from burning while letting it sweeten inside its papery shell. Avoid overcrowding the pan, since crowded vegetables will steam instead of roast, which reduces caramelization.
Create a hole in the center and place feta block, drizzle with remaining olive oil. Roast until zucchini is tender and feta is caramelized, about 30-35 minutes.: During roasting you will see the edges of the zucchini and onion turn golden and the block of feta take on a slightly browned, blistered surface. The kitchen will fill with a savory, slightly sweet aroma and you may hear gentle sizzling as moisture evaporates. That caramelization adds complexity and depth to the soup. If the top is browning too quickly, loosely tent with foil to prevent burning while the interiors finish cooking. Check for tenderness with a fork, and remove when the zucchini feels soft through to the center.
Remove herbs and squeeze out roasted garlic. Transfer vegetables and cheese to the blender; add broth (use less for a thicker soup) and blend until smooth. Warm on the stove when ready to serve if you want it hot or eat chilled. Ladle soup into bowls; garnish with extra feta and fresh dill, plus a drizzle of olive oil, if desired.: After the pan cools just enough to handle, pull out the thyme and oregano sprigs to avoid woody stems in the blender. Squeezing the roasted garlic releases a sweet, spreadable paste that dissolves into the soup, providing mellow umami. The roasted garlic should be soft and slightly caramel in color; if it still resists, give it a couple more minutes. Watch for any charcoal black bits which indicate over-roasting, and discard those cloves if present.
Transfer vegetables and cheese to the blender; add broth (use less for a thicker soup) and blend until smooth.: When you pulse the blender, you will see a glossy, homogeneous mixture form, and the aroma will become intensely inviting. The texture should be smooth and slightly thickened by the roasted solids, with the feta melted into a creamy emulsion. Blending in batches ensures even processing, and you should scrape down the sides to incorporate any bits clinging to the container. A common error is adding too much broth at once, which can thin the soup more than intended; start with less and add until you reach your desired consistency.
Warm on the stove when ready to serve if you want it hot or eat chilled.: Gently warming the blended soup over medium low heat lets the flavors knit without risking separation. You may notice a gentle steam and a soft bubbling at the edges as it warms, which is the cue to stir frequently to prevent scorching. If serving chilled, allow the soup to cool to room temperature before refrigerating in an airtight container, which preserves the bright herbal notes. Avoid boiling the soup vigorously, as that can dull fresh flavors and sometimes make the texture grainy.
Ladle soup into bowls; garnish with extra feta and fresh dill, plus a drizzle of olive oil, if desired.: The final presentation should show a smooth surface, small crumbles of salty feta , and flecks of bright dill . The drizzle of olive oil adds a glossy finish and a fragrant top note. Serve immediately for the best contrast between warm soup and cool herb garnish. A common serving mistake is overgarnishing, which can overwhelm the delicate roasted base; a light sprinkle is usually enough.