Heat oven to 375°F. In a large bowl, whisk together flour, baking powder, baking soda, sugar and salt. Using a pastry blender or two knives, cut in butter until mixture resembles small peas. In a medium bowl, whisk together buttermilk, ricotta and dill; stir into flour mixture. On a lightly floured surface with floured hands, pat out dough to 1-inch thickness.
Using a 3-inch biscuit cutter, cut out biscuits. Push together dough scraps and shape into more biscuits. Place biscuits, 1 inch apart, on a baking sheet.
Bake until puffed and golden, 25 to 30 minutes. Transfer sheet to a wire rack and let cool slightly. Serve warm.