Heat 2 tablespoons of the olive oil in a 10-inch nonstick saute pan over medium heat. Add the pasta and stir until warmed through, 2 to 3 minutes.
Meanwhile, beat the eggs with the milk in a large bowl. Add the Parmesan and sprinkle with salt and pepper. Stir to combine.
Add the pasta to the egg mixture. Stir to combine.
Add the remaining tablespoon of olive oil to the same pan and swirl to cover the bottom. Add the egg and pasta mixture, cover, and cook over medium-low heat until the edges of the frittata begin to brown and the center is set and slightly puffed, about 15 minutes.
To serve, slide the frittata onto a cutting board and slice into wedges.