Preheat oven to 450 degrees. In a large bowl, whisk together flour, sugar, salt, pepper, baking powder, and baking soda, 30 seconds. Toss butter into mixture to evenly coat, then press between your fingers to create flower-petal shapes.
Stir together buttermilk and relish; slowly pour over flour-butter mixture, stirring with a fork, until a crumbly dough forms. Transfer to a parchment-lined baking sheet. Gather dough with your hands, pressing firmly to bind, and flatten into a 6-by- 10-inch rectangle. Lift parchment along a short end of dough and fold in half, forming a 6-by-5-inch rectangle. Turn dough 90 degrees; gently reflatten to 6 by 10 inches. Fold in half again and flatten slightly into an 8-inch square.
Cut dough into fourths in both directions with a large, sharp knife to form 16 square biscuits. Brush tops with buttermilk. Bake until puffed, golden brown on top, and hollow-sounding when tapped on bottoms, 16 to 18 minutes. Transfer to a kitchen towel-lined basket; cover to keep warm.