In a liquid measuring cup, combine yeast, water, and 1 tablespoon sugar. Set aside until mixture becomes creamy and foamy, about 5 minutes.
Meanwhile, in a large bowl, whisk together flour, remaining sugar, baking powder, baking soda, and salt. Using a pastry cutter or two knives, cut shortening into dry ingredients until mixture resembles coarse meal.
Add yeast mixture and buttermilk and stir until dough just comes together. Turn dough out onto a lightly floured work surface and knead 5 or 6 times; dough should be soft and moist. Return dough to bowl, cover bowl with plastic wrap, and refrigerate overnight or up to 1 week.
Turn dough out onto a heavily floured work surface. Knead dough about 10 times. Using a lightly floured rolling pin, roll dough out to ⅓-inch thickness. Using a 2¼-inch round cutter, cut biscuits as close together as possible. Gather dough scraps and place one on top of the other. Knead and roll out dough again. Stamp out as many biscuits as possible. (Biscuits made from the scraps will not be as fluffy.)
Arrange biscuits, with sides touching, on an ungreased baking sheet. Brush with melted butter and set aside to rise in a warm place for about 30 minutes.
Meanwhile, preheat oven to 425 degrees F. Bake biscuits until golden brown, 10 to 12 minutes. Serve warm.