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.
Pour in the buttermilk and stir until just combined. Do not overmix.
Drop spoonfuls of biscuit dough onto the filling, spreading them out evenly.
Bake in the preheated oven for about 20-25 minutes or until the biscuits are golden brown and the filling is bubbly.
Allow the pot pie to cool for a few minutes before serving. Scoop out portions with both the biscuits and the filling.