Preheat your oven to 375°F. Spray a 13x9-inch baking dish with nonstick spray and set it aside. This will prevent sticking and make for easier cleanup later.
In a large bowl, combine the cooked, shredded chicken, cream of chicken soup, mixed frozen vegetables, minced garlic, ground black pepper, shredded mozzarella cheese, and grated mild cheddar cheese. Stir everything together until the mixture is well combined and evenly distributed.
Spread the chicken and vegetable mixture from Step 2 evenly into the prepared baking dish. Make sure the top is level so the biscuits will bake evenly later.
Open the canned biscuits and cut each biscuit into quarters. Place all biscuit pieces in a large bowl. Drizzle the melted butter over the biscuit pieces and toss them to coat evenly. I like to make sure every piece gets a good coating of butter so they bake up nice and golden.
Carefully transfer the baked biscuit pieces from Step 4 and arrange them evenly over the chicken mixture in the baking dish. Place the dish back in the oven and bake, uncovered, for 20 to 25 minutes, or until the biscuits are golden brown and the casserole is bubbly.
Let the casserole cool for a few minutes before serving to ensure it's safe to eat and the filling has a chance to set slightly. Serve and enjoy!