Preheat oven to 375°F (190°C) and grease a muffin tin or line with paper liners.
In a large bowl, whisk together cornmeal, flour, sugar, baking powder, and salt.
In another bowl, mix milk, honey, melted butter, and eggs until combined.
Pour wet ingredients into dry ingredients and stir until just combined.
Fold in chopped jalapeños and cheddar cheese if using.
Divide batter evenly into muffin cups, filling about ¾ full.
Bake for 15–18 minutes until golden and a toothpick comes out clean.
Remove from oven and let muffins cool in the pan for a few minutes.
Transfer to a wire rack and drizzle with extra honey if desired.
Serve warm and enjoy.