In a mixing bowl, stir together flour, baking powder, salt, soda, and sugar.
Using a pastry blender or two knives, cut shortening into flour mixture until fine crumbs form.
Stir in starter until a soft dough forms and cleans the sides of the bowl.
With your hands, gather dough into a ball and gently knead in bowl for about 30 seconds.
On a lightly floured board, roll dough into a 1/2-inch-thick circle; cut dough into biscuits with a 2-inch-round cutter.
Place biscuits 2 inches apart on ungreased baking sheets, lightly brush tops with melted butter, and let rest for 15 minutes.
Bake in a 425° oven for 12 minutes or until tops are golden brown.