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