Prep your pan and oven. Heat your oven to 400°F (200°C). Line a 12-cup muffin tin with liners or grease it well.
Grate and drain the zucchini. Use the large holes of a box grater.
Place the zucchini in a clean towel and squeeze out excess moisture. Removing water keeps the muffins from becoming soggy.
Mix the dry ingredients. In a large bowl, whisk together cornmeal, flour, baking powder, baking soda, salt, sugar, and pepper.
Whisk the wet ingredients. In a separate bowl, whisk eggs, buttermilk, oil, and honey. If you’re using milk and yogurt, whisk in the apple cider vinegar too.
Combine wet and dry. Pour the wet mixture into the dry.
Stir gently with a spatula until just combined. The batter should be thick but scoopable.
Fold in the zucchini and corn. Add the squeezed zucchini and corn kernels. If using cheese and chives, fold them in now.
Don’t overmix—streaks of flour are okay.
Portion the batter. Divide evenly among the muffin cups. Fill each cup about 3/4 full for nicely domed tops.
Bake. Bake for 14–18 minutes, until the tops are golden and a toothpick comes out clean or with a few moist crumbs.
Cool. Let the muffins rest in the pan for 5 minutes, then transfer to a rack to cool. They firm up as they cool, making them easier to handle.
Serve. Enjoy warm with butter, a drizzle of hot honey, or alongside soup, eggs, or salad.