1Heat 2 tbsp butter in a large skillet over medium-high heat. Season chicken with salt and pepper, then brown in batches until lightly colored on the outside, about 3 minutes per batch. Transfer to a plate.
2Add remaining 2 tbsp butter to the skillet. Sauté onion, celery, and carrot until softened, about 5 minutes.
3Sprinkle 3 tbsp flour over vegetables and stir constantly for 1 minute to cook out the raw taste.
4Pour in chicken broth and cream, stirring to dissolve any stuck bits. Add the cooked chicken back to the skillet along with thyme and frozen peas. Simmer for 8–10 minutes until chicken is cooked through and filling is thick. Taste and adjust seasoning.
5While filling simmers, make biscuits: Whisk together 2 cups flour, baking powder, and salt in a bowl. Cut in 6 tbsp cold butter with your fingertips until mixture resembles coarse crumbs. Stir in milk until a soft dough forms.
6Preheat your oven to 400°F.
7Drop biscuit dough by large spoonfuls over the hot filling, spacing them a couple inches apart. They don't need to cover the whole top.
8Bake for 12–15 minutes until biscuits are golden brown and filling bubbles at the edges.