Fill a saucepan with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the pasta then return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through but is still firm to the bite, about 10 minutes. Stir in the frozen peas then cook for 1 more minute; drain well in a colander set in the sink. Return the pasta and peas to the saucepan.
Mix in the eggs, 2 tablespoons of Parmesan cheese and black pepper; cook over low heat, stirring constantly until the eggs are cooked through, 2 to 3 minutes. Serve sprinkled with 1 teaspoon of Parmesan cheese.