1. Preheat oven to 400°F. Place potatoes in a small saucepan, cover with cold water and add a pinch of salt. Bring to a boil over high heat. Reduce heat and simmer until just tender, about 10 minutes. Drain.
2. Beat eggs and milk together; season with salt and pepper. Warm oil in a large, ovenproof nonstick skillet over medium heat. Cook leeks, stirring, until softened, about 5 minutes. Add turkey and sauté until cooked through, about 3 minutes. Reduce heat to low, mix in potatoes and season with salt and pepper.
3. Pour egg mixture into skillet, tilting pan so it runs around the edges. Cook undisturbed until bottom is firm, about 10 minutes, periodically lifting sides to let egg flow under. Place in oven and bake until center is firm, 8 to 10 minutes. Sprinkle cheese over top. Cut into wedges; serve.