Preheat the oven to 475 degrees Fahrenheit, and spray an 8” round cake pan with cooking spray.
In a medium bowl, combine the self-rising flour, salt, and sugar and whisk to mix well. Add the shortening and, using your fingers, rub it into the flour mixture until there are no lumps bigger than a large pea.
Stir in the heavy cream and buttermilk, taking care not to overmix. Let stand for 2-3 minutes. The dough will be very wet, resembling large-curd cottage cheese.
Pour the all-purpose flour into a shallow bowl or pie plate. Rub your hands in the flour to dust them well. Using a ¼-cup measuring scoop or something of similar size, spoon a lump of wet dough into the flour, and sprinkle some flour over it to coat well. Gently pick it up and shape it into a soft round. I do this by cradling it in the cupped palm of one hand and gently shaking it, letting the excess flour fall through my fingers. You can also toss the dough softly - very softly - back and forth from cupped palm to cupped palm: it should feel similar to a water balloon. Place biscuit in pan and repeat with remaining dough, pushing biscuits tightly against one another so that they will rise up and not spread out.
Brush with melted butter and bake until set and lightly browned, 15-20 minutes. Cool for a minute or two, then dump out and break apart into individual biscuits.