Preheat oven to 500°. Use a nonstick cake pan or baking sheet.
Cut the shortening and butter into about 1/2-inch chunks, place in a small bowl and put in the refrigerator or freezer. Let chunks chill for about 15 minutes.
Whisk flour and sugar together in a large mixing bowl. Add cold chunks of butter. Using a pastry blender or your fingertips, break-up the chunks a little. Add the shortening, and continue to cut and break-up the chunks until they are about the size of a pea.
Make a well in the center and pour in the buttermilk and cream. Start at the sides of the bowl and use a spatula or wooden spoon to toss the flour over the milk. Continue to work the flour from the sides of the bowl, just until the dough comes together. If the dough starts to pull away from the sides of the bowl and sticks to your fingers, you have the right amount of buttermilk. If there are dry spots and the dough is not sticky when you touch it, add more buttermilk.
Dust all-purpose flour on a surface and turn dough onto surface. Flour your hands. Cuddle the dough by pressing your hands along the outer edges of the dough. Pat and press the top of the dough with your floured hands. Flour the top a bit if it is sticky. Fold the dough in thirds, and then roll it– starting at one end– into a ball. Pat and fold again. Dust with a bit of flour if it is sticky. Repeat this two or three times so that the dough on the outside feels less sticky and becomes smooth.
Use a rolling pin or pat the dough with your hands to achieve desired thickness, about 1/2-inch thick.
Using a small biscuit cutter (2-inch), cut the biscuits without twisting the cutter. Place biscuits so they touch if you like soft sides, or about a 1/2-inch apart for more crisp sides.
Take the leftover pieces of dough and cuddle them with your hands, handling the dough as little as possible. Cut the biscuits. With the remaining scraps, make a snake and place it around the edges of the biscuits. This edge makes the biscuits along the edges rise more evenly. And the snakes make a crispy extra for the cook.
Bake biscuits in center of oven until they are a light golden brown, about 8 to 10 minutes. Brush the tops with melted butter.
* If you are not using self-rising flour, add 1 tablespoon of baking powder and 1 teaspoon of fine sea salt.