01 - Preheat oven to 400°F. Grease a 9x13-inch casserole dish with butter or cooking spray.
02 - In a large skillet over medium heat, melt 3 tablespoons butter. Add diced onion, carrots, and celery; sauté for 5-6 minutes until softened.
03 - Sprinkle 3 tablespoons flour over the vegetables and cook, stirring constantly, for 1 minute to form a roux.
04 - Gradually whisk in chicken broth and milk while stirring. Add dried thyme, salt, and pepper. Bring to a simmer and cook for 3-4 minutes until thickened.
05 - Stir in diced cooked chicken, frozen peas, and frozen corn. Remove from heat and transfer the mixture to the prepared casserole dish.
06 - In a mixing bowl, whisk together 2 cups flour, baking powder, and 1/2 teaspoon salt. Cut in cold cubed butter until mixture resembles coarse crumbs. Stir in 3/4 cup milk until just combined, being careful not to overmix.
07 - Drop spoonfuls of biscuit dough evenly across the chicken mixture surface.
08 - Bake for 25-30 minutes until biscuits are golden brown, cooked through, and the filling is bubbling at the edges.
09 - Remove from oven and let cool for 10 minutes before serving.