Preheat the oven to 375°. In a 12-inch, nonstick ovenproof skillet, heat 2 tablespoons of the olive oil. Add the onion and cook over moderate heat until softened, about 5 minutes. Add the scallions and potatoes and cook until heated through, about 2 minutes. Add the remaining 1/4 cup of olive oil and swirl to coat the pan with oil.
In a bowl, whisk the eggs with the cream, salt and paprika. Pour the eggs into the skillet, add half of the cheese and cook over moderate heat, stirring, until the side of the frittata begins to set, about 2 minutes. Using a spatula, lift the side of the frittata away from the pan to allow the uncooked egg to seep underneath. Cook over moderate heat until the side is browned, about 6 minutes.
Sprinkle the top with the remaining cheese and bake the frittata for about 14 minutes, until set. Turn on the broiler and broil the frittata for 1 to 2 minutes, until the top is lightly browned. Slide the frittata onto a large plate and let stand for 5 minutes. Cut into wedges and serve warm or at room temperature.