01 - Preheat the oven to 400°F. Grease an 8-inch square baking pan or a 9-inch round skillet with butter or cooking spray.
02 - In a large bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt until evenly blended.
03 - In a separate medium bowl, beat the eggs, then whisk in the milk, vegetable oil, and melted butter until the mixture is smooth and well combined.
04 - Pour the wet ingredients into the dry ingredients. Stir gently with a spatula or wooden spoon until just combined. Be careful not to overmix—some small lumps are fine.
05 - Gently fold in the chopped jalapeños, corn kernels, and shredded cheddar cheese until evenly distributed throughout the batter.
06 - Pour the batter into the prepared baking pan or skillet. Use a spatula to spread it evenly into the corners.
07 - Bake for 22 to 25 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
08 - While the cornbread bakes, combine the honey, lime juice, lime zest, and a pinch of salt in a small saucepan over low heat. Warm gently for 2 to 3 minutes, stirring occasionally until the mixture is fluid and fragrant.
09 - Remove the cornbread from the oven. While still warm, drizzle the lime honey glaze evenly over the top. Allow to cool for 5 to 10 minutes before slicing into squares and serving.