Preheat oven to 350˚F (180˚C). Heat oil in large skillet set over medium heat; cook eggplant, zucchini, red pepper, onion, garlic, and 1/2 tsp (2 mL) salt and pepper for 12 to 15 minutes or until vegetables are tender. Let cool slightly.
Whisk together eggs, milk, and remaining salt and pepper. Stir in 1 cup (250 mL) cheese, eggplant mixture, tomatoes and parsley.
Melt butter in 10-inch (25 cm) ovenproof nonstick skillet set over medium heat. Pour egg mixture into pan; cook for about 5 minutes or until eggs start to set around edges. Sprinkle with remaining cheese.
Return to oven. Cook for 10 to 15 minutes or until eggs are set. Turn out onto cutting board or serving dish. Cut into wedges.