Place a rack in the middle third of the oven; preheat the oven to 425 F.Generously grease a large baking sheet or coat with nonstick spray.
Thoroughly stir together 3 cups flour, the sugar, Rumford Baking Powder, baking soda, and salt in a large bowl. Sprinkle the butter over the flour mixture. Cut in using a pastry blender, forks, or the fingertips until the butter is incorporated in very fine bits; scrape up the flour underneath to be sure it is evenly incorporated. (Alternatively, combine the flour, sugar, baking powder, baking soda, and salt in a food processor fitted with a steel blade. Process in 4 or 5 on/off pulses to blend the ingredients. Sprinkle the butter over the flour mixture. Process in on/off pulses until the butter is in very fine bits; scrape up the flour underneath to be sure it is evenly incorporated. Turn out the flour-butter mixture into a medium bowl.)
Being very careful not to over-mix, gently stir 1 1/3 cup buttermilk into the flour-butter mixture until the dough just comes together; if necessary, add enough more buttermilk to produce a soft, moist dough. Sprinkle evenly with 11/2 tablespoons flour. Knead in the bowl 5 or 6 times to form a smooth mass, adding a little more flour to prevent stickiness, if necessary. Let stand 1 minute. With flour-dusted hands, shape and smooth the dough into a flat discup Generously dust a large sheet of wax paper or baking parchment with flour and center the dough on it. Evenly dust the dough with a little more flour. Top with another sheet of paper. Press or pat out the dough into a generous 1/2-inch thick round; it should be evenly thick. Peel off the top sheet, then lightly pat it back into place. With the paper layers still attached, flip over the dough; peel off and discard the second sheet.
Using a 3 1/2- to 4-inch round cutter (or a wide-mouthed glass or discarded 28-ounce vegetable or fruit can) dipped in flour, cut out the shortcake rounds. Dip the cutter in flour as needed. Re-combine the dough scraps and continue forming rounds until all the dough is used. Space the rounds about 2 inches apart on the baking sheet.
Bake in the middle third of the oven for 10 to 15 minutes, or until the biscuits are nicely browned on the top and bottom (lift up one to check). Transfer to a wire rack and let cool. Store airtight for up to two days; or freeze for up to three weeks. (Thaw before using.) Makes about 7 large biscuits, up to 12 smaller ones.
For the berries: At least 1 hour before serving time and up to 8 hours if preferred, in a non-reactive bowl combine the chopped berries with sugar; use the larger amount for tart berries. The sugar will gradually dissolve and berries will release their juices and become soupy.
To serve: At serving time, using a bread knife or other large serrated knife, split the biscuits in half horizontally. Center the bottom half of each on a serving plate, cut side up. Top each half generously with the berries, then place the biscuit tops over the berries and press down lightly. Spoon a few more berries over the tops, if desired, then garnish each dessert with a generous dollop of whipped cream. Add a few whole berries or berry halves to the plates, if desired.