Preheat your oven to 425°F. In a mixing bowl, combine the flour, baking powder, sugar, and salt. Using a box grater, grate the chilled butter directly into the dry ingredients. Work the butter in gently with your fingers until the texture resembles coarse crumbs. Pour in the milk and mix lightly with a fork just until a rough dough begins to form. Transfer the dough to a floured surface and fold it over a few times to build layers. Press it into a slab about 1 to 2 inches thick. Use a biscuit cutter, a drinking glass rim, or simply a knife to slice the dough into 6 to 8 biscuits. Set aside.

In a large oven-safe skillet or Dutch oven, melt the butter over medium heat. Toss in the minced shallots, garlic, and sprigs of thyme. Cook for about 5 minutes until fragrant and softened. Add in the carrots, celery, and 1 teaspoon of salt. Continue to sauté for another 5 minutes, allowing the vegetables to start tenderizing. Sprinkle in the flour and stir, letting it cook for 1 to 2 minutes to eliminate any raw taste.

Pour in the wine and let it bubble briefly to cook off the alcohol—expect the mixture to thicken. Slowly stir in the chicken broth, milk, and heavy cream in increments, allowing the sauce to smooth out between additions. After a few minutes, the filling should have a thick, soup-like consistency. Stir in the shredded chicken and frozen peas. Season the mixture with the remaining salt, freshly ground black pepper, and a small squeeze of lemon juice to brighten the flavor. Discard the thyme sprigs.

Arrange the prepared biscuits over the surface of the filling in a single layer. Brush the tops with a bit of milk or melted butter to help them brown beautifully. Transfer the pan to the oven and bake for 15 to 20 minutes, or until the biscuits are golden and the filling is bubbling at the edges. Let the pot pie rest for 10 minutes before serving. Add extra salt and pepper to taste just before dishing up.