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 mixing bowl, whisk together the flour, cornmeal, sugar, baking powder, and salt until well combined.
03 - In a separate bowl, beat the eggs, then whisk in the milk, vegetable oil, and melted butter until smooth and fully incorporated.
04 - Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined, being careful not to overmix the batter.
05 - Gently fold in the chopped jalapeños, corn kernels, and cheddar cheese if using, until evenly distributed throughout the batter.
06 - Pour the batter into the prepared pan or skillet and spread evenly with a spatula.
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 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 until fluid and fragrant.
09 - Remove the cornbread from the oven. While still warm, drizzle the lime honey glaze evenly over the top. Let cool for 5 to 10 minutes before slicing and serving.