Preheat the oven to 450°F. Put 1 tablespoon of butter in a 10-inch iron skillet and set aside.
Lightly spoon the self-rising flour into a measuring cup and level it off. Don't pack it. Pour into a large bowl.
Grate the cold butter directly into the flour with a hand grater. Sprinkle a little flour over the butter to separate the pieces, then stir until evenly distributed.
Add 2 cups of buttermilk and stir gently just until the flour is moistened. If dry flour remains, drizzle in more a splash at a time, up to 2 1/2 cups. Stop stirring as soon as the dough comes together. Do not overmix.
Turn the dough out onto a floured counter. Sprinkle flour on top and pat down. Fold the dough over and turn it 3 to 4 times, flouring as needed, to create layers.
Using your hands (no rolling pin), press the dough to about 1 inch thick.
Dip a biscuit cutter in flour and press straight down without twisting. Cut biscuits as close together as possible. Gather scraps, pat out, and cut again.
Place the skillet in the hot oven for about 2 minutes until the butter melts. Swirl to coat the bottom.
Arrange the biscuits in the skillet, starting with one in the center, leaving a touch of space between them.
Bake at 450°F for 10 to 13 minutes until golden on top (about 12 1/2 minutes in my oven).
Brush the hot biscuits with melted butter.