Preheat your oven to 350 degrees.
Line a muffin tin with baking cups and spray with cooking spray. Set aside.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, and salt.
In a medium bowl, whisk together the eggs, milk, and melted butter.
Make a well in the dry mixture and pour in the wet mixture. Mix just until combined.
Fold in the zucchini and 1/2 cup of the cheddar cheese.
Spoon the cheesy cornbread zucchini muffin batter into the prepared muffin tin, filling each space 3/4 of the way full. Sprinkle the tops with the remaining cheddar cheese.
Bake for 20 minutes.
Let cool on a cooling rack.
Store at room temperature in an air-tight container for 3 days or freezer up to 3 months.