Preheat broiler to high.
Crack eggs in a large bowl, add Parmigiano, some salt and pepper and beat thoroughly.
Heat a medium-sized skillet over medium-high heat with 1 turn of the pan of EVOO, about 1 tablespoon. Add cooked pasta and toss to coat in the oil. Add beaten eggs, stir and then let them sit. Once you see eggs getting firm on the sides of the skillet transfer to the broiler and cook for another few minutes or until the eggs are firm in the center.