Freeze butter in advance. Preheat oven to 450°F. Line a baking sheet with parchment paper. Set aside
In a large mixing bowl, use a whisk to sift together flour, sugar, baking powder, baking soda, salt and cayenne pepper.
Use a box grater to shred frozen butter on the medium side of the cheese grater. Use a fork to stir the butter shreds into the flour mixture until evenly distributed.
To the bowl add 2 cups cheddar cheese and fresh chives. Stir until coated with flour and evenly distributed.
Make a well in the center of the flour mixture, pour in the buttermilk. Use a rubber spatula to gradually mix the buttermilk into the dry ingredients until fully absorbed. (You may need to bring the dough together using your hands toward the end of mixing.)
Turn dough out onto a lightly floured nonstick surface. Turn a couple of times to bring together and lightly coat with flour, just enough until it's no longer sticky.
Press or roll the biscuit dough into an 8 or 10-inch circle 3/4-inch thick. Using a sharp knife dipped in flour, cut into wedges.
Place wedges 2-inches apart on the prepared pan. Brush the tops with melted butter and sprinkle with reserved 1/2-cup cheese. (Reserve some butter for after baking).
Place pan into the oven. Bake for 16-18 minutes or until the tops are golden brown.
Serve immediately brushed with additional butter or transfer to a wire rack to cool.