Preheat the oven to 400 degrees F (200 degrees C).
Heat oil in a 12 inch skillet over medium-high heat. When the skillet is hot, add the potatoes, and fry until crispy and golden, about 15 minutes. Reduce heat to medium, and add onions. Cook, stirring, until softened. Season with salt and pepper. Pour eggs over the potatoes and onions.
Place the skillet in the oven for about 10 minutes, or until eggs are firm. Remove from the oven, and sprinkle shredded cheese over the top. Return to the oven for about 5 minutes, or until cheese is melted.
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