Preheat the oven to 475 degrees F.
Sift the self-rising flour, cake flour, baking powder, baking soda, sugar, and salt into a large bowl. Using your fingers or a pastry cutter, work the 4 tablespoons cold butter into the flour until the pieces are pea size. Add the buttermilk to the flour mixture and, with your hands or a rubber spatula, stir just until the milk and flour come together to form a dough. Sprinkle some of the all-purpose flour on a work surface and place the dough on top of the flour. Using your hands, press the dough into a 1/2-inch-thick disk about 8-inches in diameter. Using a 3-inch round cutter dusted with flour, cut out dough rounds. Be sure to press straight down when cutting the dough (a twisting motion will prevent the dough from rising). You will need to reform the scraps of dough to make 8 biscuits. Do this by pushing the scrap pieces together and pressing them into a 1/2-inch-thick disk.
Place the biscuits on a small sheet pan and brush the tops with the 2 tablespoons melted butter. Bake in the oven for 10 to 12 minutes, or until golden brown. Allow to cool briefly.