In a large skillet, melt the butter over medium heat. Add the carrots, celery, and cook until the vegetables are slightly softened.
Add Flour and Spices:
Stir in the flour, salt, pepper, and thyme. Cook for 2 minutes, stirring constantly.
Gradually Add Liquids:
Gradually whisk in the chicken broth and milk. Continue stirring until the mixture thickens.
Add Chicken and Peas:
Add the cooked chicken and frozen peas. Stir until well combined. Remove from heat.
Transfer to Baking Dish:
Pour the chicken and vegetable mixture into a greased baking dish.
For the Biscuit Topping:
Prepare Biscuit Dough:
In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Add the cold, cubed butter and use a pastry cutter or your fingers to cut the butter into the dry ingredients until it resembles coarse crumbs.
Add Buttermilk:
Pour in the buttermilk and stir until just combined. Do not overmix.
Form Biscuits:
Drop spoonfuls of biscuit dough onto the filling, spreading them out evenly.
Bake:
Bake in the preheated oven for about 20-25 minutes or until the biscuits are golden brown and the filling is bubbly.
Serve:
Allow the pot pie to cool for a few minutes before serving. Scoop out portions with both the biscuits and the filling.