Place a rack in the center of your oven and preheat to 425°F.

Add the buttermilk and stir gently to combine, being careful not to overmix. If the batter is still very dry, add more buttermilk, 1 tablespoon at a time, until it just comes together—I added 1 additional tablespoon.

Turn the dough onto a work surface (no need to flour it) and knead 3 times, until it comes together. Pat into a 1-inch-thick square that is about 6x6 inches and cut into 8 or 9 biscuits with a bench scraper or sharp chef’s knife. When cutting, be sure to only press directly down with your knife or cutter; do not saw back and forth or you will seal the flaky layers and they won’t expand. Transfer the biscuits to a plate, cover, and chill in the fridge until you’re ready to bake.

For the filling, heat 1 tablespoon oil in a large oven-safe skillet or Dutch oven over medium heat. Add the chicken, sprinkle with a pinch of salt, and cook until browned on all sides, about 2 minutes per side. Transfer chicken to a plate (it will not be cooked through yet).

Heat the remaining 1 tablespoon olive oil in the skillet. Add the onion and celery and cook, stirring, until softened, about 5 minutes.

Add the garlic, thyme, and salt and cook for 1 minute, until fragrant. Add the wine and bring to a boil, scraping up the bottom of the skillet. Simmer for about 2 minutes, until the liquid is mostly reduced.

Return the chicken to the skillet and sprinkle everything with the flour. Stir to coat the chicken and veggies in the flour and cook for about a minute, until toasty-smelling.

Slowly add about half of the broth, a splash at a time, stirring constantly, until thick. Add the remaining broth and the milk. Stir well and bring to a simmer. Add the frozen vegetables and stir well. Turn off the heat.

Arrange the biscuits on top of the pot pie. Brush the tops with milk and sprinkle with flaky salt if you like. Bake for 20 to 25 minutes, until hot, golden, and bubbly. Cool for 5 to 10 minutes before serving.