Preheat your oven to 350°F (175°C). Grease a standard 9x13 inch casserole dish or an 8x8 inch square baking dish (for a thicker casserole).

Prepare the broccoli: If using fresh broccoli, chop the florets and steam or blanch them until they are crisp-tender (about 3-4 minutes). Drain thoroughly. If using frozen broccoli, you may use it straight from the freezer.

In a large mixing bowl, combine the can of condensed soup, mayonnaise (or sour cream), chopped onion (if using), onion powder, salt, and pepper. Stir well until the mixture is smooth and evenly combined.

Gently fold the 1 cup of shredded cheddar cheese into the soup mixture.

Add the prepared broccoli florets to the cheese and soup mixture. Use a rubber spatula to fold the broccoli into the base, ensuring all the florets are coated evenly.

Pour the entire mixture into the prepared casserole dish, spreading it into an even layer.

Prepare the topping: In a separate small bowl, combine the crushed cracker crumbs and the 4 tablespoons of melted butter. Stir until the crumbs are thoroughly coated. Sprinkle the buttery cracker mixture evenly over the top of the casserole base, followed by the remaining 1/4 cup of shredded cheddar cheese.

Bake the casserole in the preheated oven for 25 to 35 minutes. The casserole is done when the edges are bubbling and the topping is golden brown and crispy. Remove from the oven and let the casserole rest for 5 to 10 minutes before slicing and serving.