Preheat the oven to 350°F. Spray a 9 x 13-inch baking pan with nonstick cooking spray.

Prepare the broccoli: cut 3–4 fresh broccoli crowns into bite-sized florets. Steam or boil until tender, then drain very well. (If using frozen broccoli, thaw or cook according to package instructions and drain/pat dry until excess moisture is removed.)

Spread the drained broccoli in an even layer on the bottom of the prepared 9 x 13 pan.

In a large mixing bowl, combine 4 tablespoons melted butter, 1 cup mayonnaise, one 10.5 oz can cream of chicken soup, and 1/4 cup diced white onion. Stir until blended.

Add 2 eggs, 1 cup shredded sharp cheddar cheese, 1 teaspoon salt, and 1/4 teaspoon ground black pepper to the bowl. Mix until the eggs and cheese are fully incorporated.

Pour or spoon the cheese mixture evenly over the broccoli in the pan, smoothing the top so the broccoli is well coated.

Sprinkle the remaining 1/2 cup shredded sharp cheddar cheese evenly over the casserole. Top with 1 sleeve crushed Ritz crackers, spreading them in an even layer.

Bake in the preheated oven for 30–40 minutes, until the casserole is hot and bubbly and the top is lightly browned.

Remove from the oven and let the casserole rest for about 5 minutes before serving.