Mix the flour, cornmeal, baking powder, baking soda, brown sugar and salt in a large bowl.
In another bowl mix together the melted butter, buttermilk, and honey until well combined. Whisk in the eggs.
Add the wet ingredients to the dry ingredients and stir just until combined. Stir in the jalapeño peppers and shredded cheese. Do not over mix; it's okay if there are a few lumps.
Pour into a greased 8’’ pan and bake in a preheated 350 degrees oven for 25 to 30 minutes or until a toothpick inserted in the center comes out with moist crumbs.
