01 - Preheat oven to 400°F. Grease or line an 8-inch square baking pan.
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 fully incorporated.
04 - Pour the wet ingredients into the dry ingredients. Stir gently until just combined, being careful not to overmix.
05 - Gently fold in corn kernels, chopped jalapeños, and cheddar cheese if using.
06 - Transfer batter to the prepared baking pan, smoothing the top evenly.
07 - Bake for 25-30 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.
09 - Meanwhile, mix powdered sugar, lime juice, and lime zest in a small bowl until smooth and drizzleable.
10 - Drizzle the lime glaze over the slightly warm cornbread. Allow to cool further, then slice and serve.