In a large pan, melt butter over medium-high heat. Add carrots, celery, onion, and cook until onions are translucent.
Sprinkle flour over vegetables and cook for 2-3 minutes, stirring.
Add salt, thyme, parsley, and chicken broth. Stir while bringing to a simmer. Continue to allow the filling to simmer while you mix up the biscuit topping.
Once the veggies are just about halfway tender (about 7-8 minutes of simmering), add the chicken to the pan along with the heavy cream. Remove from the heat and pour into a 9 by 9 inch baking dish.
For the Biscuit Topping
In a medium bowl, mix flour, baking powder, salt, thyme, and parsley together.
Cut in cubed butter with a pastry cutter until you have pea-sized bits of flour-coated butter.
Slowly stir in the milk as you mix the dough together.
Top the prepared filling with an even layer of one-inch pieces of the biscuit dough.