Preheat the oven to 350F and lightly grease a 9"x9" baking pan.
Grate enough zucchini so that you obtain 2 cups when lightly packed in measuring cups. Squeeze out excess water from the zucchini. (see notes)
In a large bowl, combine the cornmeal, flour, baking powder, salt, and basil. Mix the dry ingredients together until well combined. Make a well in the center.
Pour the milk in the center of the dry ingredients. Add to the milk, the melted butter and the egg. Mix only the wet ingredients together first, before starting to bring the dry ingredients into them.
Stir the wet and dry ingredients together with a large spoon of rubber spatula. Mix until there is no more dry mixture noticeable, making sure not to overmix.
To the batter, add the drained zucchini, chopped onion, bell pepper, garlic, and 1 cup of the grated cheese. Fold the ingredients into the batter until well combined.
Place the batter into the greased baking pan. Use your rubber spatula or spoon to evenly spread the batter into the pan. Sprinkle the remaining ¼ cup of cheese on top of the casserole.
Place the casserole into the preheated 350F oven. Bake for 35 minutes, or until a toothpick inserted in the middle comes out clean. If using an 8"x8" baking pan, the casserole might take an extra 5 minutes to bakes, testing for doneness with a toothpick.
When fully baked remove the casserole from the oven and let rest for 5-10 minutes before cutting into squares.