Put oven rack in middle position and preheat oven to 375°F.

Whisk together eggs, cayenne (if using) salt, and pepper until just combined.

Heat oil in an ovenproof 9- to 10-inch heavy nonstick skillet over high heat until very hot but not smoking. Add potatoes stirring once, then cover and cook until beginning to brown, about 4 minutes. Lower heat to medium-high, stir potatoes and cook another 3-4 minutes. Add the scallions and continue to cook covered another 2 minutes. Stir potato mixture, then cover and cook 3 minutes more or until potatoes are tender.

Pour beaten eggs evenly over potato mixture and crumble cheese over eggs. Transfer skillet to oven and bake frittata, uncovered, until set and just cooked through, about 15 minutes.

Let cool slightly, serve frittata directly in skillet or invert onto a plate.