Position rack in center of oven and preheat the oven to 475º F.
Sift the self-rising flour, cake flour, sugar, baking powder, salt, and baking soda into a medium mixing bowl.
Using your fingers or a pastry cutter, work the cold butter into the flour until there are no butter pieces larger than a pea.
Add the heavy cream to the flour mixture and, using your hands or a rubber spatula, stir just until the cream and flour come together to form a dough. Do not overmix!
Sprinkle some of the all-purpose flour on a flat 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 dipped in flour, cut the dough into circles. Be sure to press straight downward when cutting the dough -- a twisting motion will prevent the dough from rising. You will need to re-form the scraps of dough in order to make 8 biscuits. Do this by gathering the scrap pieces together and pressing to re-form into a 1/2-inch thick disk, then cut as many additional biscuits as possible from the re-formed dough.
Place the biscuits on a small baking sheet and use a pastry brush to brush the tops with the melted butter.
Bake in the oven for 10 to 12 minutes, or until golden brown.
Using oven mitts or pot holders, remove the biscuits from the oven and allow to cool briefly and serve while still warm.
YIELD: Eight 3-inch biscuits