Preheat oven to 350°F Coat a 2-quart square baking dish with nonstick cooking spray. Spread hash brown potatoes and broccoli evenly in bottom of prepared baking dish; top with turkey bacon or ham. Set aside.
In a medium bowl, gradually stir milk into flour. Stir in egg product, half of the cheese, the basil, black pepper, and salt. Pour egg mixture over vegetables.
Bake for 40 to 45 minutes or until a knife inserted near the center comes out clean. Sprinkle with remaining cheese. Let stand for 5 minutes before serving.