01 - Preheat oven to 400°F. Grease or line an 8-inch square baking pan with parchment paper.
02 - In a large bowl, whisk together cornmeal, flour, sugar, baking powder, and salt until well blended.
03 - In a separate bowl, whisk milk, eggs, melted butter, vegetable oil, and honey until smooth and emulsified.
04 - Pour the wet ingredients into the dry mixture. Stir gently with a spatula until just combined, being careful not to overmix.
05 - Gently fold in corn kernels, chopped jalapeños, and cheddar cheese if using.
06 - Pour batter into the prepared baking pan, smoothing the top evenly with a spatula.
07 - Bake for 25 to 30 minutes until golden brown and a toothpick inserted in the center comes out clean.
08 - Remove from oven and let cool in the pan for 10 minutes before glazing.
09 - While cornbread cools, whisk powdered sugar, lime juice, and lime zest in a small bowl until smooth and pourable.
10 - Drizzle the lime glaze over the slightly warm cornbread. Allow to cool further, then slice into squares and serve.