Heat oven to 375 degrees. Spray mini muffin tins with nonstick cooking spray.
In large bowl, beat eggs, milk, salt, pepper and basil to blend well. Stir in mixed vegetables and Parmesan cheese.
Fill prepared pans with egg mixture. Bake until egg mixture puffs and is just set in center, about 8-10 minutes. With rubber spatula, loosen frittatas from muffin cups and slide onto platter.