Preheat oven to 450°F.: The kitchen should feel warm from the oven and you may notice a slight rise in ambient heat which helps hold the skillet hot when you transfer it. Setting a high oven temperature ensures the braising finishes quickly and helps the butter sauce reduce without overcooking the potatoes. A common mistake is not allowing the oven to fully reach temperature, which can extend baking time and soften the crust. Make sure the oven reads at 450°F before you put the pan in.
Cut both ends off each of the peeled potatoes so that they sit flat, they should be about 2 inches tall. Pat dry with a paper towel and season each side with salt and pepper.: When you cut the ends, you expose a clean flat surface that will make full contact with the pan, producing more even browning. Patting the potatoes dry is crucial because moisture prevents the development of a crisp crust, and the surface should feel dry to the touch. You will smell the raw potato starch as you work and see dry, matte surfaces once patted. Avoid leaving them wet on the surface or the sear will steam instead of crisping.
Place the avocado oil in a large heavy-bottomed skillet over medium-high heat. Once the oil is shimmering, add the potatoes flat side down. Cook until a golden crust has formed, about 5 minutes.: You'll know the pan is ready when the avocado oil shimmers and moves fluidly across the skillet. As the potatoes sear, listen for a steady, low sizzle, and watch the edges begin to brown and take on a deep golden color. That crust provides texture and flavor; resist turning them too early or the crust will not develop. If the potatoes stick badly, the pan was not hot enough or they were not dry.
Flip the potatoes, and continue to cook for another 3-4 minutes until a crust has formed on the other side. Drain the oil from the skillet.: After flipping, you'll again hear the sizzle and see the crust deepen. The aroma will become butterier and nuttier as the surface caramelizes. Draining the oil prevents the pan from becoming greasy when you add the butter and broth; too much oil can make the sauce slick rather than silky. A pitfall here is overcrowding the pan, which lowers the surface temperature and prevents browning, so give each potato space.
Add the butter, garlic cloves, thyme, and rosemary to the skillet. Pour in the vegetable stock, and transfer the skillet to the oven.: When you add the butter and herbs, you should hear a gentle hiss as the butter melts and releases an herbaceous aroma. The garlic will begin to perfume the fat, creating a fragrant base for the braising liquid. Pouring in the vegetable broth introduces steam, which will finish cooking the potatoes from the inside. The oven will take over, and you may notice the pan bubbling softly as the sauce reduces. Avoid using a skillet that is not oven safe, or you could damage the pan or cause a safety issue.
Bake for 25-30 minutes or until the potatoes are tender when pierced with a fork.: During baking, the aroma in your kitchen will shift to a warm, herby butter scent as the broth reduces and the potatoes steam. Test doneness by inserting a fork into the center; it should meet little resistance and feel almost creamy. If the fork meets resistance, bake a few minutes longer, checking every five minutes. A common error is relying on time alone rather than checking tenderness, since potato sizes vary and ovens differ slightly.
To serve, top with flaky sea salt and spoon the remaining butter sauce in the pan over the potatoes.: Right before serving, the pan will be glossy with a concentrated butter and herb sauce. Spoon this sauce over the potatoes so each bite gets a hit of salty, buttery flavor and a hint of herb. The finishing touch of flaky sea salt gives a satisfying crunch against the soft interior. Be careful not to over salt at this stage; taste a small piece first if you are unsure about the seasoning.