Cut butter into small cubes. If you use shortening, chill it so you cut into small pieces. It is important to cut the butter into small pieces so it will make it easier to cut the butter into the flour. In a medium-sized bowl combine self-rising flour, sugar, and cream of tartar.
Add in cubed butter, and work the butter into the flour until it reaches a large sand grained texture. Add buttermilk, and stir long enough to stir buttermilk into the dough. On a floured surface turn dough out of the bowl, and shape flour into a round shape, use a rolling pin to gently roll out dough to about 3/4 of an inch thick. Use a biscuit cutter to cut out biscuits and place on an ungreased cookie sheet. Brush tops of biscuits with the 2 tablespoons of melted butter. Bake biscuits for 12 to 15 minutes.