Place a rack in the middle of the oven and preheat to 450 degrees F. Generously coat an 8- to 8 1/2-inch round cake pan, pie tin, or similar-size round baking pan with butter or nonstick cooking spray.
Thoroughly stir together 1 3/4 cup flour, Rumford Baking Powder, baking soda, salt, and sugar in a medium-sized bowl. Sprinkle the butter over the flour mixture. Cut it in using pastry blender, forks or fingertips until the mixture is the consistency of coarse meal and only fine bits of butter remain. Being very careful not to overmix, gently stir in a scant 1 cup buttermilk until the dough is just blended; if necessary, add enough more buttermilk to produce a very soft, moist dough, stirring as little as possible. Let it stand a minute or two. Sprinkle over a tablespoon of flour. Knead the dough once or twice to form a smooth mass.
Sprinkle more flour on a sheet of wax paper, then turn the dough out onto it. Lightly sprinkle the dough with a bit more flour. Top with second sheet of wax paper. Pat down until the dough is smooth and a scant 1-inch-thick all over. Dip a 2 1/4- to 2 1/2-inch round cutter or similar-size small glass into flour. Punch out (don't twist) biscuits, dipping the cutter in flour between each one. Brush off excess flour. Transfer the biscuits to the pan, spacing very close together. Brush excess flour from the dough scraps. Gently press the scraps together. Continue punching out biscuits until all the dough is used. Brush the biscuit tops generously with softened butter.
Bake on the middle rack for 13 to 16 minutes, until biscuits are puffed and tops are nicely browned. Remove for the oven and let stand for 5 minutes, then serve immediately.