For the zucchini cornbread: Preheat the oven to 350 degrees F. Butter a 9-inch cast-iron skillet.
Whisk together the flour, cornmeal, sugar, baking powder, baking soda, 1 ¼ teaspoons kosher salt and several grinds of pepper in a large bowl. Whisk together the melted butter, buttermilk and eggs in a small bowl until smooth. Pour the butter mixture into the cornmeal mixture and stir until thoroughly combined.
Put the zucchini in a clean kitchen towel and squeeze out any excess moisture; discard the liquid. Fold the zucchini, corn and chives into the batter, then pour into the prepared skillet and bake until a cake tester comes out clean and the top is a deep golden brown, about 40 minutes. Let cool for 15 minutes before serving.
For the honey butter: While the cornbread is cooling, mix together the butter and honey in a small bowl until smooth. Smear onto slices of cornbread and sprinkle with a pinch of flaky salt.
