Step 1Heat the broiler. In a 10-inch nonstick skillet, heat 2 tablespoons olive oil over medium heat. Add the onion and cook until it softens, about 5 minutes. Add the zucchini and cook until it's no longer moist and begins to clump together, about 10 minutes. Remove from the heat.
Step 2While the zucchini is cooking, beat the eggs with a fork until they are ropy and well-mixed but not foamy.(They should be somewhat light in color.) Stir the cheese, salt and basil leaves into the egg mixture and then add the cooked zucchini. Stir for a minute after you've added the zucchini in order to cool it slightly.
Step 3Return the pan to the heat and add the remaining 2 tablespoons olive oil. When the oil is hot, pour in the egg mixture and immediately reduce the flame to medium low. The bottom of the egg mixture should set very quickly. Gently lift the sides with a fork and pull them toward the center, allowing the loose egg mixture to run underneath. Cook this way until the eggs are almost set, about 5 minutes. The mixture should look like very loose scrambled eggs, with a little liquid remaining.
Step 4Place the pan under the broiler until the eggs are puffed and lightly browned, about 45 seconds. Cool slightly before carefully sliding the frittata onto a serving plate. Serve warm or at room temperature.