Preheat the oven to broil.
Heat oil in a skillet over medium-high heat; add garlic, cook for 1 minute. Do not allow garlic to brown, or it will turn bitter. Add zucchini; cook 5 minutes or until tender, stirring continuously. Season with salt and pepper.
Meanwhile, whisk together the eggs, egg whites, and rosemary, and season with salt and pepper. Pour the egg mixture over the zucchini and cook, just until the eggs begin to set, about 3 minutes.
Sprinkle cheese evenly over the top. Place pan under the broiler for 3 minutes or until the fritatta rises slightly and becomes light and settled. The eggs should not be runny. Transfer to a serving plate, cut into pie-shaped wedges, and serve.