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.