Preheat the oven to 450°F.
Add flour, salt, sugar, baking soda and baking powder to a large mixing bowl. Mix.
Add butter and shortening. Rub butter into flour with your fingers until all the pieces are about pea size, working quickly as not to melt the butter.
Make a well in the middle of the flour mixture. Pour in the buttermilk. Fold the flour into the milk using a spatula until a dough form. The dough should be slightly wet, this will yield moist biscuits.
Turn dough out onto a well-floured board. Pat dough into a disk with the heel of your hands. Fold dough in 1/2 and pat out into a disk again. Repeat folding and flattening 4 more times.
Then pat the dough out to about 1-inch thick.
Cut with a 3-inch round biscuit cutter. Gather the scraps, pat out into a new disk and continue cutting. This will form 6 biscuits.
Place biscuits on a baking sheet, about 1/4-inch apart on all sides so they can support each other when they rise in the oven.
Brush the top of biscuits with buttermilk. Sprinkle with sugar or turbinado sugar for a little more sweetness or skip for savory biscuits.
Place in preheated oven and bake for about 15 minutes, until tops are golden brown.
Transfer biscuits to a large bowl and wrap in a towel until ready to serve.