Add broccoli, mayonnaise, sour cream, 1 cup grated sharp cheddar cheese, condensed cream of mushroom soup, beaten eggs, garlic powder, salt, and pepper. Mix together. Then, transfer this mixture to the prepared casserole dish. Top with the remaining ½ cup grated sharp cheddar cheese and crushed crackers. Cover with aluminum foil. Bake in the preheated oven for 20 minutes. Then, remove the foil and bake for an additional 10 minutes until golden brown. Serve immediately.