Preheat oven to 450 (make sure you do this first). It's really important that you work these biscuits as quickly as possible and get them RIGHT INTO THE OVEN! It will help the rise and texture so much if you do --
In a large mixing bowl, combine all dry ingredients. Work in butter and shortening with your fingertips until it is all broken up evenly (this might be effective in the food processor, but I haven't tried it). Feel free to squish it into the dry mix until it's all sort of rubbed in and no clumps are left. Work as quickly as you can to minimize softening the fat.
Make a well in the center of your dry goods/fat combination and pour the buttermilk into the center. Start with just one cup and mix it all in by hand. If the dough isn't just almost so sticky it can't be worked, add more buttermilk (this is going to depend on many factors, including the weather and the mood of your flours).
Flour your work surface (I like to use sweet rice flour) lightly and turn out your super sticky dough. Turn it into itself (like a knead, but more gentle) 5 or 6 times, just until it comes together.
Push the dough out into a round that is about 1 inch thick. The best biscuits come from an evenly thick dough, but they are kind of forgiving, so don't worry over it too much if it's close. Find something round with an approximate measurement of 2" -- biscuit cutter would be great, but I don't own one, so I just use a cup that has a similar diameter (be sure to grease it REALLY good or that dough will never come out).
Push your 2" round thing down through the dough completely before twisting to release. Put biscuits on a greased glass dish (pyrex type critter), so that they're touching but not squished together. Brush the tops with butter (or spray lightly with pan spray) and bake for 20 minutes for a soft biscuits, 30-35 for a hard biscuit.
Let rest at least 10 minutes for structure to set, then eat until they make you sick. This will make 9-16 biscuits, depending on the size of your cutter and the thickness of your biscuits.