Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper or a silicone liner.
Whisk together the flour, corn meal, sugar, chives, baking powder, and salt.
Add the butter, and mix with a pastry blender or a fork until the mixture forms coarse crumbs.
Stir in the buttermilk and cheese, mixing until thoroughly moistened.
Transfer the dough to a lightly floured surface. Knead 4 or 5 times, just until the dough comes together.
Roll out the dough to 3/4-inch thickness. Use a 2-inch biscuit cutter to cut into rounds. Gather and re-roll the dough once and continue cutting out biscuits.* Place the biscuits on the prepared pan, leaving about 2 inches between each.
Bake 12 to 15 minutes or until golden brown. Place the pan on a wire rack to cool.
Brush the tops of the warm biscuits with melted butter.
Notes
*Your yield may vary depending on how efficiently you cut out the biscuits.
Store in an airtight container at room temperature up to 2 days.