Preheat oven to 450˚F. Whisk together the flour, baking powder, baking soda, sugar and salt in a bowl. Using a pastry cutter, work the cold butter nto the flour mixture until the butter is the size of small peas.

Add the buttermilk, Cheddar and chives to the flour-butter mixture and stir with a fork to form a loose dough.

Turn the dough out onto a floured surface and gently pat into a 6x9-inch rectangle. Fold into thirds as you would a letter and pat into a 6x9-inch rectangle again. Dip the edges of a 3-inch round biscuit cutter in flour and punch out 6 biscuits from the dough. Transfer the biscuits to a parchment paper-lined baking sheet. If you have any remaining dough scraps form into another biscuit or two; they won't rise as high, though. Brush the tops with heavy cream and bake until lightly browned, 14-16 minutes.

Serve warm.