Melt the butter in a medium microwave-safe mixing bowl and set aside to cool to room temperature.
In a large, separate bowl, whisk together the cornmeal, flour, baking powder, baking soda, and salt.
Add the eggs to the bowl with the melted butter and whisk until blended. Stir in the buttermilk and honey. Add the wet ingredients to the dry ingredients and, by hand, stir gently just until combined. The batter will be lumpy. Gently stir in 1 cup of the cheese, corn, jalapeño peppers, and half of the green onions. Let the batter sit at room temperature for 20 minutes while you preheat the oven.
Place a rack in the center of your oven and preheat the oven to 350 degrees F. Pour the batter into the prepared pan and smooth the top. Sprinkle the remaining green onions and 1/2 cup cheese on top. Bake the cornbread for 28 to 32 minutes, or until center is set, the top is golden brown, and a toothpick inserted in the center comes out clean. Let cool in the pan, then using the parchment paper, lift it onto a cutting board. For tidy slicing, let cool completely. For warm, messy slices, cut right away and enjoy!
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