Bring a large pot of salted water to a boil. Add the spaghetti and cook for about 5 minutes or half of the cooking time instructed on the package. Drain in a colander and immediately place under cold running water to cool thoroughly.

Meanwhile, in a large bowl, add the eggs and Parmigiano and season with a little salt and a few grinding of pepper. Whisk well to combine. Add the spaghetti to the bowl and toss to coat thoroughly.

In a 12-inch non-stick skillet over medium heat, heat the olive oil. Pour in half of the spaghetti mixture and spread it out evenly. Cook, shaking the pan occasionally, until the underside turns lightly golden brown and sets, about 5 to 7 minutes.

Arrange the mozzarella and tomato slices over the spaghetti and scatter the basil over the top. Give the remaining spaghetti mixture a quick stir, then pour it over the top and spread it out evenly to cover.

Place a large enough plate over the top of the pan to cover. Carefully flip the frittata over onto the plate and then slide it back into the pan. You can use pot holders or oven mitts to help you, if you like. Cook, shaking the pan occasionally, until the underside turns lightly golden brown and sets, about 5 to 7 minutes.

Serve warm or, even better, at room temperature sliced into wedges, either wrapped in paper towels to enjoy in hand or accompanied by a small green salad for a light meal or snack.