Preheat the oven to 375 degrees. Remove the seeds from and slice jalapeno finely. Set aside.
In a medium bowl, stir sugar, honey and butter together. Whisk in egg. Whisk in baking soda and buttermilk. Add salt, cornmeal, and flour. Do not over-mix. As soon as the flour disappears, stop mixing. Fold in sliced jalapeno and shredded cheddar cheese.
Add batter equally to the cups of a greased or lined muffin tin, filling to the top. Bake for 15-20 minutes. Prick the center of one muffin with a toothpick and make sure it comes out clean. If not clean, bake for about 5 more minutes.