In a large non-skillet over medium-high heat, melt the butter. Sauté the onion, pepper, and mushrooms for 3-4 minutes or until the vegetables begin to soften. Add the ham and continue to cook until the veggies are soft. Lower heat to medium-low.

In a bowl, beat the eggs. Pour the eggs into the skillet and cook and scramble them until they are no longer runny and are as done as you like. Sprinkle with cheese if desired.

Serve immediately.