Preheat oven to 375°F (190°C) and grease a 9×13-inch baking dish or line with parchment paper.
Grate zucchini using a box grater and squeeze out as much moisture as possible using a clean kitchen towel.
In a large bowl, whisk together cornmeal, flour, baking powder, baking soda, salt, and black pepper.
In another bowl, whisk eggs, buttermilk, melted butter, and honey until smooth.
Add drained zucchini, shredded cheese, and corn kernels to the wet mixture and stir gently.
Add dry ingredients to the wet mixture and mix just until combined.
Pour batter evenly into the prepared baking dish and smooth the top.
Bake for 35–40 minutes until golden and a toothpick inserted in the center comes out clean.
If browning too quickly, loosely cover with foil during the last 10 minutes.
Let rest for 10 minutes before slicing and serving.