Preheat the oven: Preheat your oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish or casserole dish with cooking spray.
Prepare the filling: In a large bowl, combine the cooked shredded chicken, cream of chicken soup, frozen vegetables, minced garlic, black pepper, shredded cheddar cheese, and shredded mozzarella cheese. Mix all the ingredients thoroughly until they are evenly blended.
Assemble the casserole: Transfer the chicken and vegetable mixture to the prepared baking dish, ensuring it is spread out evenly.
Prepare the biscuits: Open the canned biscuits and place them evenly over the chicken filling. Depending on the size of your baking dish, you may need to slightly overlap the biscuits or arrange them neatly to cover the top of the casserole.
Brush with butter: Brush the tops of the biscuits with the melted butter to help them bake to a beautiful golden color.
Bake the casserole: Place the casserole in the preheated oven and bake for 25-30 minutes, or until the biscuits are golden brown and fully cooked, and the filling is bubbling around the edges. If the biscuits are browning too quickly, cover the casserole loosely with aluminum foil during the last 10 minutes of baking.
Serve and enjoy: After baking until perfectly done, take the casserole out of the oven and allow it to sit for a few minutes. Serve the Chicken Pot Pie with Biscuits warm, and enjoy the creamy, cheesy filling with the flaky, buttery biscuits on top.