In a large bowl, combine flour, salt, baking soda and cream of tartar. Mix with a whisk until well combined. Work shortening into dry mixture using hands or a pastry cutter, until pea-sized crumbs form. Pour in buttermilk, using one hand to mix the dough and one hand to turn the bowl. Turn dough out onto a generously floured flat surface. Flour hands and dough. Pat dough into a 1" thick rectangle. Generously spread softened butter over dough to within 1" of the edges. Fold dough as follows: Take left side and fold to the middle, take right side and fold to the middle, fold top down to the middle and fold bottom edge up to the middle. Give the dough a 45° turn and pat dough again into a 1" thick rectangle, re-flouring dough and surface as needed. Repeat folding process 2 more times, gently and quickly, being careful not to overwork dough. Cut dough using a 2" biscuit cutter and place rounds on a parchment-lined baking sheet, making sure biscuits touch each other. Bake for 10 to 15 minutes, until tops of biscuits are golden brown. Brush tops of biscuits with melted butter and serve immediately.
Makes about 1 dozen.