Preheat the oven to 400°F (200°C). Grease the 9x9 inch baking dish with cooking spray or butter.
In a mixing bowl, combine the cornmeal, all-purpose flour, baking powder, salt, and sugar. Whisk to blend the dry ingredients thoroughly.
In another bowl, mix the buttermilk, vegetable oil, and eggs until well blended.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
Gently fold in the corn kernels and chopped jalapeños.
Pour the batter into the prepared baking dish and spread it evenly.
Bake in the preheated oven for 25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
While the cornbread is baking, prepare the honey glaze by melting the butter in a small saucepan over low heat. Stir in the honey until well combined.
Once the cornbread is done baking, remove it from the oven and immediately brush the honey glaze over the top using a rubber spatula or brush.
Allow to cool for a few minutes, then cut into squares and serve warm.