Preheat oven to 400 degrees F (205 degrees C). Grease a 9x13 inch baking dish.
Melt the butter in a skillet over medium heat, and cook the onion until tender.
Spread Cheddar cheese in the bottom of the prepared baking dish. Layer with mushrooms, olives, sauteed onion, ham, and jalapeno peppers. In a bowl, scramble eggs together with milk, and season with salt and pepper. Pour egg mixture over ingredients, but do not stir.
Bake, uncovered, in the preheated oven for 30 minutes, or until no longer runny in the center and slightly brown on top. Allow to cool slightly, then cut into squares and serve.