Preheat oven to 350 degrees F (175 degrees C). Lightly grease a 9×13 inch baking dish.
Heat a lightly oiled skillet over medium high heat. Add the potatoes and cook for 10 minutes, until lightly brown. Layer in bottom of prepared pan.
Add butter to skillet and saute broccoli and onions until soft; spoon over potatoes. Spread ham on top of broccoli and onions.
In a large bowl, beat together eggs and cheese. Season with salt and pepper and pour over vegetables.
Bake in preheated oven until eggs are set and lightly brown on top, about 20 to 30 minutes. Serve warm.
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