Melt butter with oil in a 12-inch ovenproof skillet over medium-high heat; add zucchini and onion, and sauté 12 to 14 minutes or until onion is tender. Remove from heat, and stir in 1/4 cup grated Parmesan cheese.
Whisk together eggs and next 3 ingredients at least 1 minute or until well blended. Pour over vegetable mixture.
Bake at 350° for 13 to 15 minutes or until set; increase oven temperature to broil, and broil 5 1/2 inches from heat 1 to 2 minutes or until edges are lightly browned. Sprinkle evenly with remaining 1/4 cup grated Parmesan cheese and basil. Garnish, if desired.
Lightened Zucchini-Onion Frittata: Reduce butter to 1 tablespoon, and omit oil. Sauté zucchini and onion as directed; remove from heat. Reduce grated Parmesan cheese to 1/4 cup, stirring 2 tablespoons into vegetable mixture. Substitute 1 (15-ounce) carton garden vegetable egg substitute for 8 eggs and 1/4 cup lowfat milk for 1/4 cup milk, and whisk together with salt and pepper. Pour over vegetable mixture. Bake as directed; do not broil. Sprinkle evenly with remaining 2 tablespoons grated Parmesan cheese and basil. Garnish, if desired.