In a large bowl, combine the flour, sugar, basil, baking powder, salt and baking soda. Beat the eggs, milk and oil; stir into dry ingredients just until moistened. Fold in zucchini.
Fill greased or paper-lined miniature muffin cups two-thirds full. Sprinkle with cheese. Bake at 400° for 12-15 minutes or until a toothpick inserted near the center comes out clean. Cool for 5 minutes before removing from the pans to wire racks. Serve warm.
Yield: about 4-1/2 dozen.