Preheat the oven to 350F.Lightly butter or oil the muffin pan.Cut jalapeño, grate cheese.
In a medium bowl, stir butter, sugar, and honey together. Whisk in eggs and buttermilk.Add cornmeal, flour, salt, and baking soda.Do not over-mix. As soon as the flour disappears, stop mixing. Fold in jalapeño and cheese.
Divide batter equally between the cups of a greased or lined muffin tin, filling almost to the top.
Bake for 25 minutes.Prick the center of one muffin with a toothpick and make sure it comes out clean.If not, bake for about 5 more minutes.