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 fully incorporated.
04 - Pour wet ingredients into dry ingredients. Stir gently until just combined, being careful not to overmix.
05 - Gently fold corn kernels, chopped jalapeños, and cheddar cheese if using into the batter.
06 - Pour batter into prepared baking pan and smooth top with spatula for even baking.
07 - Bake for 25-30 minutes until golden brown and a toothpick inserted in center comes out clean.
08 - Remove from oven and let cool in pan for 10 minutes before glazing.
09 - In a small bowl, whisk powdered sugar, lime juice, and lime zest until smooth and creamy.
10 - Drizzle lime glaze over warm cornbread. Allow to cool further, then slice into squares and serve.