Preheat oven to 375 degrees. Whisk together flour, baking powder, baking soda, and salt in a medium bowl. Cut in butter using a pastry blender or your fingertips until mixture resembles coarse meal. Add buttermilk and cream; stir to combine.
Turn out dough onto a lightly floured work surface, and pat into a 6 1/2-inch round (about 1 inch high). Using a lightly floured 2 1/2-inch cutter, cut out rounds. Transfer to a baking sheet lined with parchment paper, spacing about 1 inch apart. Gather scraps, reshape, and cut out. Brush tops with buttermilk. Bake until tops are golden, 22 to 24 minutes. Transfer biscuits to a wire rack, and cool.