Preheat oven to 450 degrees. Line baking sheets with parchment paper.
In a large bowl, whisk together flour, baking powder, salt, sugar and baking soda.
Add shortening and butter and cut in with a pastry cutter until the flour mixture resembles small peas.
Add buttermilk to the flour mixture and stir together to form a shaggy, sticky dough with no flour remaining. Do not over mix.
Sprinkle your work surface with flour. Turn dough onto prepared work surface. Dust your hands with flour. Lightly dust top of dough with flour. Pat dough with hands to form a 1/2 inch thick rectangle about 11x7 inches. Fold rectangle into thirds, as if you were folding a letter. Pat the dough out again into an 11x7 rectangle and refold. Repeat this a third time, then pat dough back out to a 1/2-inch thick rectangle.
Using lightly floured 2-1/4 inch round cookie cutter, cut dough and place smooth side up on the baking sheet. Space biscuits about 3/4 inch apart. Stack and reshape the scraps and cut out more biscuits until all dough is used. Refrigerate, uncovered, 15 minutes.
Bake chilled dough until tops are golden brown and lightly crisped, 15-20 minutes. (Less time if you skipped the chilling step...). Let biscuits cool on pan 5 minutes.
Enjoy!