Stir together the warm water, yeast and 1 tsp. sugar in a small bowl. Let stand for 5 minutes.
Stir together the flour, 3 T. sugar and next three ingredients in a large bowl. Cut the butter and shortening in with a pastry blender or 2 forks until crumbly. Stir in the buttermilk and yeast mixture until just flour mixture is moistened. Cover bowl with plastic wrap and refrigerate at least 2 hours or up to 5 days.
Preheat oven to 400°F. Put dough onto a lightly floured surface and knead 3 or 4 times. Roll dough into a 1/2-inch thick circle; fold in half; repeat.
Cut biscuits with a 3-inch round cutter. Reroll remaining scraps and cut with cutter. Place on a parchment paper lined baking sheet with sides touching. Brush with 3 tablespoons of the melted butter.
Bake in oven for 15 to 20 minutes until golden. Brush with remaining 3 tablespoons butter and enjoy.