Preheat oven to 425 degrees.
Whisk together flour, baking soda, baking powder, salt, and sugar.
Using a food processor with dough attachment, or a pastry cutter, cut butter and shortening into flour mixture. If you're using a food processor, using pulse about 3 times should be enough. If you're using a pastry cutter, do it just until it starts to look like very coarse crumbs.
Pour buttermilk into flour/butter mixture and mix until just combined. If you're using a food processor, a few pulses again should be enough.
Pour the mixture out onto a well floured surface.
Gently pat out the dough into a large circle, about 1-2" thick, then fold the dough in half 3-5 times, until it just starts to come together. Gently pat the dough out into another large circle, about 1.5" thick. NOTE: For this step I wear plastic gloves to help prevent the warmth of my hands from melting the butter, and because it's so messy.
Use a biscuit cutter to cut out as many biscuits as possible. Place these on an ungreased baking sheet, with the sides touching each other.
Gently push the remaining dough together to cut out more biscuits. Place these biscuits on the baking sheet, again with sides touching each other. NOTE: These biscuits will not be as fluffy as the first cut biscuits.
Bake for about 12-15 minutes, or until tops start to golden. Remove from oven and rub melted butter on tops of biscuits.