01 - Preheat oven to 400°F. Grease a 9x13 inch casserole dish with butter or cooking spray.
02 - Melt 3 tablespoons butter in a large skillet over medium heat. Add diced onion, carrots, and celery. Sauté for 5-6 minutes until vegetables are softened.
03 - Sprinkle 3 tablespoons flour over the sautéed vegetables. Stir constantly for 1 minute to combine.
04 - Gradually whisk in 2 cups chicken broth and 1 cup milk, stirring continuously to avoid lumps. Add dried thyme, salt, and black pepper. Bring mixture to a simmer and cook for 3-4 minutes until sauce thickens.
05 - Stir in cooked chicken, frozen peas, and frozen corn. Remove from heat and transfer entire mixture to the prepared casserole dish.
06 - In a mixing bowl, whisk together 2 cups flour, 1 tablespoon baking powder, and ½ teaspoon salt. Cut in cold cubed butter until mixture resembles coarse breadcrumbs. Stir in ¾ cup milk until just combined. Do not overmix.
07 - Drop spoonfuls of biscuit dough evenly across the surface of the chicken mixture.
08 - Bake for 25-30 minutes until biscuit topping is golden brown and cooked through, and filling is bubbling at the edges.
09 - Remove from oven and allow casserole to cool for 10 minutes before serving.