Heat 5 Tbsp. of the oil in a very large nonstick or cast-iron skillet. Add the potatoes and sweet potatoes and cook over medium heat, stirring frequently, until they're cooked through and golden, about 20 minutes. Separate any slices that stick together so they'll cook evenly. When done, transfer to a bowl with a slotted spoon.
If no oil remains in the pan, add another tablespoon and saute the onions until they're lightly browned. Add the onions to the potatoes and sweet potatoes and season well with salt and pepper. Add the beaten eggs.
Wipe out the pan, then return to stove and add 2 Tbsp. oil. Pour in the egg and potato mixture, smooth down any potatoes that stick up, and cook over low heat until golden on the bottom, about 10 minutes. Invert the frittata onto a plate, slide it back into the pan, and cook until set, a few minutes.
Served with a fresh green salad, this is the perfect meal.