01 - Preheat the oven to 400°F. Grease an 8-inch square baking pan or 9-inch round skillet lightly with butter or cooking spray.
02 - In a large mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt until thoroughly blended.
03 - Crack the eggs into a separate bowl and beat lightly. Whisk in the milk, vegetable oil, and melted butter until smooth and fully incorporated.
04 - Pour the wet mixture into the dry ingredients. Stir gently with a spatula or wooden spoon until just combined, being careful not to overmix.
05 - Gently fold the chopped jalapeños, corn kernels, and cheddar cheese if using into the batter until evenly distributed.
06 - Pour the batter into the prepared pan, using a spatula to spread it evenly into corners.
07 - Bake for 22 to 25 minutes until the top is golden brown and a toothpick inserted into 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 until fluid and fragrant, stirring occasionally.
09 - Remove the cornbread from the oven. While still warm, drizzle the lime honey glaze evenly over the top. Allow to cool slightly for 5 to 10 minutes before slicing and serving.