In a separate large mixing bowl, whisk together flour, sugar, baking powder, baking soda, and salt until no lumps remain. Cut the butter and shortening into the flour with a pastry cutter until it resembles coarse crumbs. Stir in yeast mixture and buttermilk until everything is just moistened. Cover and refrigerate for at least 2 hours.
Preheat oven to 400F. Line a baking sheet with parchment paper.
Turn the dough onto a lightly floured surface. Roll out to about ½" thickness and use a small round cookie cutter to cut rounds out. Transfer to the prepared baking sheet. Brush each biscuit with butter.
Bake for 15 - 20 minutes or until puffed and golden brown.
If you have more dough, reroll and repeat steps.