Preheat oven – Heat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Prepare broccoli – Blanch fresh broccoli in boiling water for 2–3 minutes (skip if using thawed frozen). Drain well.
Mix filling – In a large bowl, stir together cream of mushroom soup, cheddar cheese, mayonnaise (or sour cream), eggs, garlic powder, onion powder, salt, and pepper until smooth.
Combine – Fold in broccoli florets until evenly coated. Transfer mixture into prepared baking dish.
Add topping – In a small bowl, combine crushed crackers with melted butter. Sprinkle evenly over the casserole.
Bake – Bake uncovered for 30–35 minutes, or until topping is golden brown and casserole is bubbly.
Serve – Let rest 5 minutes before serving warm.