Peel and slice potatoes very thinly. Place in an ovenproof skillet along with the oil and rosemary. Sprinkle with salt to taste. Cook over medium-low heat, stirring occasionally, until potatoes are cooked through and some are crispy and browned, about 25 minutes.
Preheat oven to 350°F.
Add beaten eggs to the potatoes. If need be, press down potatoes so that they're covered. Season with salt and pepper and top with cheese. Continue to cook on the stove for 5 minutes.
Place frittata in the oven for 10 minutes, or until cheese is melted and the eggs are set.