Preheat oven to 375°.
Press Greek Baking-Powder Piecrust into a 10-inch quiche dish coated with cooking spray. Combine eggs and egg whites in a medium bowl; beat well with a whisk. Brush 2 tablespoons egg mixture over crust; set remaining egg mixture aside. Bake at 375° for 7 minutes; cool on a wire rack.
Heat oil in a large nonstick skillet over medium heat. Add garlic; sauté 30 seconds. Add chopped tomato, tomato paste, salt, and sugar; sauté 15 minutes or until thick (mixture will have a pasty consistency). Remove from heat; stir in thyme, basil, and pepper.
Add milks to remaining egg mixture in bowl; beat well. Stir in tomato mixture. Arrange sliced tomatoes in bottom of prepared crust; spoon egg mixture into dish. Sprinkle with cheeses. Bake at 375° for 45 minutes or until knife inserted near center comes out clean.