Grease a 9 x 13 baking pan with cooking spray. In a medium bowl, combine the chicken, potatoes, broccoli, mayonnaise, black pepper, salt, and garlic.
Spread mixture evenly into prepared baking pan. Sprinkle Parmesan and cheddar cheese on top.
Place pan in a preheated oven, 375, and bake for about 45 minutes, or until chicken is cooked through and potatoes are tender. *Adjust time according to potato size.