Heat the olive oil in a nonstick omelet pan over medium-high heat. Add the potatoes and onions and saute until tender, about 3 minutes. Gently stir in the ham and peppers and cook for an additional 2 minutes.
In a large bowl add the eggs and whisk until well blended. Stir in the grated cheese and mix to combine. Add the egg and cheese mixture to the pan, season with salt and pepper, to taste, and stir gently with a heat-proof spatula. Reduce the heat to low and cook until the egg begins to thicken, about 2 minutes. Put the pan in the oven until eggs are set and slightly puffed and brown on top, about 5 minutes.
Remove from the oven and garnish with fresh parsley. Transfer to a serving platter, cut into wedges and serve warm or at room temperature.