01 - Preheat oven to 400°F. Grease or line an 8-inch square baking pan with parchment paper.
02 - In a large bowl, whisk together cornmeal, flour, sugar, baking powder, and salt until well blended.
03 - In a separate bowl, whisk milk, eggs, melted butter, vegetable oil, and honey until smooth and emulsified.
04 - Pour wet ingredients into dry ingredients. Stir gently with a spatula until just combined, being careful not to overmix.
05 - Gently fold in corn kernels, chopped jalapeños, and shredded cheddar cheese until evenly distributed throughout the batter.
06 - Pour batter into prepared baking pan and smooth the top surface with a spatula for even baking.
07 - Bake for 25 to 30 minutes until golden brown and a toothpick inserted in the center comes out clean.
08 - Remove from oven and allow to cool in the pan for 10 minutes before glazing.
09 - While cornbread cools, whisk powdered sugar, lime juice, and lime zest in a small bowl until smooth and creamy.
10 - Drizzle lime glaze evenly over the slightly warm cornbread. Let set for 5 minutes, then slice into squares and serve.