01 - Preheat the oven to 400°F. Grease an 8-inch square baking pan or 9-inch round skillet with butter or cooking spray.
02 - In a large mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt until evenly blended.
03 - In a separate bowl, beat the eggs thoroughly, then whisk in the milk, vegetable oil, and melted butter until smooth and fully incorporated.
04 - Pour the wet ingredients into the dry mixture. Stir gently with a spatula or wooden spoon just until combined; avoid overmixing to prevent tough texture.
05 - Gently fold in the chopped jalapeños, corn kernels, and shredded cheddar cheese (if using) until evenly distributed throughout the batter.
06 - Transfer the batter to the prepared pan, spreading it evenly with a spatula to ensure uniform baking.
07 - Bake for 22 to 25 minutes until the top is golden brown and a toothpick inserted in the center comes out clean.
08 - While cornbread bakes, combine honey, lime juice, lime zest, and salt in a small saucepan over low heat. Warm gently for 2 to 3 minutes, stirring until fluid and fragrant.
09 - Remove cornbread from the oven. While still warm, drizzle the lime honey glaze evenly over the surface. Allow to cool slightly in the pan before slicing and serving warm.