Heat the oil and saute the sliced potatoes and onions a few minutes, stirring now and then but not constantly. You want everything cooked through, about 8 minutes, and for the potatoes to be a bit browned.
Stir in the garlic and basil (or whatever herb you’re using). Pour the eggs over the potatoes and onion, sprinkle the cheese on top and salt and pepper. Cover the pan and cook over medium low heat until set, about 10 minutes.
Slice the frittata onto a plate, then hold the pan over the top of the plate while you flip the plate upside down, so that the frittata ends up bottom side up in the pan. Return to the burner and cook a few minutes. Alternately, rather than flip it over you can slide the pan under a preheated broiler for 2-3 minutes until the top is lightly browned. Let it sit a few minutes at least. Then slice and serve.