Preheat oven to 450 degrees F.
Line a baking sheet or a cake pan with parchment paper or lightly butter the surface with about 1 teaspoon of the melted butter.
Combine the flour, baking powder and salt in a bowl.
Add the shortening and cut it into the dry ingredients using two knives, a pastry blender or your hands. Work the shortening in well, until it is reduced to pea-size pieces.
Add the buttermilk and mix briefly, just to incorporate it. It is very important not to overwork the dough, or the biscuits will not be delicate and light.
Gently mix in the cheddar and black pepper. The dough will be fairly sticky.
Place the dough on a smooth, well-floured surface and pat with your hands to about ¾ inch thick.
Cut out the biscuits, using a 2-inch round glass or cookie cutter. Dip the cutter into flour between cuts to keep it from sticking.
Place the biscuits on or in the prepared pan.
The remaining dough may be gently gathered together and rolled out again for more biscuits.
Brush the tops with the remaining melted butter.
Place the biscuits in the oven and bake for about 10 minutes, or until the tops are golden brown.
Remove from the oven and serve warm.