Preheat oven to 450 degrees. In a large bowl, whisk together the flour, baking powder, baking soda, salt, and sugar. Add the butter and shortening and working quickly, use your fingertips or a pastry blender to work the fat into the flour until the mixture resembles a coarse meal. Add the buttermilk and stir with a spatula to form a soft dough. Transfer the dough onto a floured surface. Pat the dough into a rough rectangle and fold it into thirds. Turn it 90 degrees, then roll and fold it again. Roll it about 1 inch thick and cut it into rounds with a biscuit cutter anywhere from 1-2 inches in diameter (or even bigger if you want to make biscuit sandwiches!) Gently gather and re-roll the scraps and cut again. Place biscuits close to each other (they can touch!) on a parchment-lined baking sheet and bake until browned and puffed, about 12-15 minutes. Brush with melted butter and serve with jam, a drizzle of honey, or sausage gravy.