Preheat oven to 450°F. Line a baking sheet with parchment.
Whisk flour, sugar, baking soda, black pepper, and cayenne in a large bowl.
Cut in the cold butter until the mixture looks like coarse crumbs with pea-sized bits.
Fold in the shredded cheddar to coat the cheese lightly with flour.
Pour in the buttermilk and stir gently just until a shaggy dough forms; do not overmix.
Turn dough onto a lightly floured surface. Pat to about 3/4-inch thickness, then fold in half and pat again.
Cut biscuits with a 2-inch cutter, pressing straight down. Gently re-form scraps and cut again.
Arrange biscuits so they touch on the sheet. Chill in the freezer for 5 minutes for extra lift.
Bake 12–14 minutes until puffed and golden at the edges.
Brush hot biscuits with melted butter. Cool 5 minutes and serve warm.