Cook spaghetti in a large pot of boiling salted water until tender but firm. Drain and refresh with cold water.
Heat oil in a large nonstick skillet over medium heat. Add onions and cook, stirring occasionally, until golden, 10 to 12 minutes. Transfer the onions to a small bowl and let cool slightly. Wipe out the pan.
Whisk together eggs, egg whites and milk in a large bowl. Stir in the onions, Parmesan, parsley, basil, salt and pepper. Add the spaghetti.
Spray the pan well with nonstick cooking spray and place over medium heat. Pour in the egg mixture and distribute evenly in the pan. Cook until the underside is golden, moving the pan around on the burner to ensure even cooking, about 6 minutes. Invert a large platter over the skillet, grasp the platter and skillet with oven mitts and carefully turn over. Lift off the skillet and spray it again with nonstick cooking spray. Slide the frittata back into the skillet and cook until the bottom is golden. Slide the frittata onto a platter. Garnish with tomatoes if using.
