Preheat oven to 375 degrees.
Place an 8-inch baking dish into oven to preheat.
Heat butter in a skillet over medium high heat. (Ask an adult for help.) Add onions and sauté (slow cook) until tender, about 3 minutes. Add ham and potatoes and sauté until they are lightly brown, another 3-4 minutes.
Remove the pan from oven. (Make sure you use pot-holders or oven-mits, since the pan will be hot!!) Transfer the onion, ham and potato mixture from skillet into the baking pan.
Pour eggs over the ingredients and stir gently. Season with salt and pepper.
Cover baking pan with foil, place in the oven and bake for 12 to 15 minutes, until the eggs set.
Remove foil cover, sprinkle grated cheese on top and place back in oven for about 5 more minutes, until the cheese melts and begins to brown.
Cut the frittata into wedges and serve.
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