It’s very European to use potatoes in omelets, tarts, and frittatas—even on pizzas. The key is to use small cubes of potato, as here, or very thin slices. You don’t want to be biting into a whole mouthful of starch, and you want your potatoes to cook through in a reasonable amount of time.
In A 9½-Inch-Diameter nonstick ovenproof skillet, heat the oil over a medium flame. Add the onion and sauté until translucent, about 4 minutes. Add the potato, garlic, salt, and pepper, and sauté over medium-low heat until the potato is tender and golden, about 15 minutes.
Preheat the broiler. In a medium bowl, whisk the eggs, cream, Parmesan cheese, prosciutto, and basil to blend. Stir the egg mixture into the potato mixture in the skillet. Cover and cook over medium-low heat until the egg mixture is almost set but the top is still runny, about 2 minutes. Place the skillet under the broiler and broil until the top is set and golden brown, about 4 minutes. Using a rubber spatula, loosen the frittata from the skillet and slide it onto a plate. Cut the frittata into wedges and serve.