Preheat your oven to 350 and line or grease a muffin tin.
Mix together the dry ingredients (flour, cornmeal, baking powder, baking soda, salt).
In another bowl, whisk the wet ingredients (milk, eggs, honey, melted oil or butter).
Shred the zucchini, then squeeze out the excess moisture with a clean towel or paper towels.
Combine the wet and dry mixtures until just blended.
Fold in the shredded zucchini and cheese.
Scoop into muffin cups and bake at 350°F for 22-25 minutes until golden and set.
Cool slightly before enjoying warm and cheesy.