In a medium-sized saucepan melt 2 tablespoons butter, then add the flour, salt, and pepper. Cook and stir until it begins to bubble. Gradually add the milk while cooking and stirring until it becomes thick and bubbly. Remove from heat and set aside to cool to room temperature before adding the cheese.

In a large skillet brown the ham or sausage. Scrape meat to the edges of the pan and melt the butter in the middle. Saute the onions, peppers, and mushrooms for about 1 minute over medium heat.

Add the eggs cooking and stirring with a silicone spatula until they just begin to set. Reduce the heat, and scrape the egg mixture from the bottom and around the edges of the pan toward the middle. This process should result in a runny, pouring consistency of partially cooked eggs. Turn off the heat and proceed to Step 4

Combine the white sauce and cheese mixture with the meat, vegetables, and eggs in the frying pan and mix thoroughly. Then pour the mixture into a buttered 9 X 13 inch casserole.

Melt the remaining butter, drizzle over the breadcrumbs while tossing with a fork or two chopsticks. Sprinkle breadcrumbs over the entire casserole.