Preheat the oven to 400°F (200°C). Place a 10-inch cast-iron skillet in the oven to heat while you prepare the batter.
In a small saucepan over medium heat, melt the butter. Continue cooking, swirling occasionally, until the butter turns golden brown and smells nutty, about 5 minutes. Remove from heat and let cool slightly.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda, and salt.
In a separate bowl, whisk the buttermilk, eggs, honey, and browned butter (reserve 1 tablespoon of the browned butter for the skillet). Pour the wet ingredients into the dry and stir just until combined — a few lumps are fine.
Carefully remove the hot skillet from the oven. Add the reserved tablespoon of browned butter and swirl to coat the bottom and sides. Pour the batter into the skillet and smooth the top.
Bake for 20–25 minutes, until the top is golden brown and a toothpick inserted into the center comes out clean.
Let cool in the skillet for 10 minutes, then slice into wedges. Drizzle with additional honey if desired and serve warm.