Steam the broccoli florets for 5-7 minutes until they are just becoming tender. Do not overcook or they will become mushy. Drain and allow to cool.
In a large mixing bowl, combine the soup, mayonnaise, onions, eggs, and 1 cup of the cheese.
Gently combine the broccoli with the sauce until everything is thoroughly mixed together.
Spread evenly into a 9x13 inch baking dish or 1.5 quart baking dish of your choice.
Sprinkle the remaining cheese over the casserole.
Melt 3 tablespoons of butter and add 1 cup of Panko bread crumbs, stirring well.
Spoon the bread crumbs evenly over the casserole.
Bake in a preheated 350-degree oven for 30 minutes until it is bubbly and lightly browned.