Preheat oven and skillet: Preheat the oven to 375°F with the rack in the middle of the oven. Place the skillet in the oven to preheat for 10 minutes.
Prepare cornbread batter: Combine the cornmeal, flour, sugar, baking powder, baking soda, and salt in a large bowl. Whisk together the buttermilk, eggs, and 2 tablespoons of melted butter in a separate bowl. Pour the wet ingredients over the dry and mix with a spatula until just combined (be careful not to overmix). The batter will be thick. Fold in the peppers, corn, and 1 cup cheese until just combined.
Pour batter into hot pan: Carefully remove the skillet from the oven, and add the remaining two tablespoons of butter. Swirl to coat the bottom and sides of the skillet. Scrape the batter into the skillet and spread with a spatula into an even layer. Sprinkle the top with remaining ¼ cup cheese.
Bake the cornbread: Bake until a toothpick inserted into the center of the bread comes out clean, 20 to 25 minutes. Serve immediately with honey and butter. Store leftovers, covered, at room temperature, for up to 5 days.
