Heat 1 tablespoon oil in large skillet over medium heat. Add the chopped onion and cook for about 3 minutes, stirring often, or until it begins to soften.
Add the red pepper and cook, stirring, for a few minutes, until the pepper begins to soften. Add the zucchini and garlic with salt and pepper to taste. Add 1 more tablespoon oil, if necessary, or 2 tablespoons water.
Cook for five to ten minutes, stirring, until the zucchini is tender but still bright green. Stir in chopped parsley. Stir the filling into the beaten eggs.
Heat 1 tablespoon olive oil in a 12-inch nonstick skillet over medium-high heat. Pour in the egg mixture and stir with a fork.
Shake the pan gently, lifting up the edge of the frittata to let the egg mixture run underneath. Reduce the heat to low, cover, and cook for about 10 minutes. The eggs should be just set.
Brown the top of the frittata under the broiler for about 2 minutes. Let cool.
Loosen the edge of the frittata from the pan with a spatula. Slide the frittata out of the pan.
Cut the frittata into diamond-shaped pieces and arrange in a decorative pattern on a serving platter.