Preheat the oven to 425°. Prepare muffin tins by buttering them if they are not non-stick.
Combine the eggs, milk and oil in a large bowl.
Combine the flour, sugar, salt, baking powder and Parmesan in another bowl. Add to the liquid mixture in batches, stirring to blend. Don't overblend!
Add the zucchini and basil and stir to blend.
Fill each muffin cup about half full. Sprinkle the top with the cheese. Bake for about 20-25 minutes for regular size muffins, 15-20 minutes for the mini muffins, until the tops are golden brown and puffy.
Serve while still warm.
NOTE: You can freeze these and pop them in a toaster oven for a few minutes for a great snack. To be honest though, they rarely survive to make it to the freezer.