Preheat the oven to 400°F. Place a 9-inch cast-iron skillet in the oven while it preheats. You can also use a greased 8x8-inch baking dish.
In a large bowl, whisk together the cornmeal, flour, sugar, baking powder, baking soda and salt. Stir in the diced jalapeño.
In another bowl, whisk together the eggs, buttermilk, honey, melted butter and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and gently stir just until combined. Don't overmix, the batter should be thick and slightly lumpy.
Carefully remove the hot skillet from the oven and add a small pat of butter, swirling to coat the bottom. Pour in the batter.
Bake for 20–25 minutes, or until the top is golden and a toothpick inserted in the center comes out with a few moist crumbs.
Mix the melted butter and honey together. Brush it generously over the hot cornbread as soon as it comes out of the oven.
Rest for 5–10 minutes, then slice and serve warm.
