Preheat the oven to 400F with a rack in the middle.
Heat the oil and 1/4 cup of water in a 10" nonstick skillet that can go in the oven. Add the potatoes, garlic, salt and pepper. Cover and let steam for 4-5 minutes. The potatoes should be just barely tender.
Remove the lid and let the water evaporate while the potatoes finish cooking, about 8 minutes, stirring now and then.
While the potatoes cook, put the eggs, cheese and a bit more salt and pepper in a small bowl and whisk or stir with a fork. (You can also add extra cheese, like grated Cheddar at this point.)
Spread the filling ingredients around and then pour in the eggs and cheese. Cook without stirring until the edges of the eggs are set, just about 1 minute. Then put the pan in the oven to finish cooking, about 10 minutes.
Slide onto a plate, cut in wedges and serve.