Preheat the oven to 400 degrees F.
Melt 3 tablespoons butter in a large skillet over medium heat. Add the diced onion, sliced carrots, and diced celery. Cook for 5 minutes until the vegetables begin to soften.
Stir in 3 tablespoons flour and cook for 1 minute. Slowly pour in the chicken broth while stirring to avoid lumps. Add the heavy cream, dried thyme, salt, and black pepper. Simmer for 3 minutes until the sauce thickens.
Add the shredded chicken and frozen peas. Stir to combine and remove the skillet from heat. Transfer the filling to a 9x9 inch baking dish.
In a mixing bowl, combine 2 cups flour, baking powder, and 1/2 teaspoon salt. Cut in the cold cubed butter until the mixture resembles coarse crumbs. Stir in the milk until a soft dough forms.
Drop spoonfuls of the biscuit dough over the filling. Bake for 20 to 25 minutes until the biscuits turn golden and the filling bubbles around the edges.