To make the dough: Sprinkle both packets of dry yeast over warm water. Set aside for 5 minutes.
In a medium size bowl, sift together flour, sugar, baking powder, soda and salt in a large mixing bowl.
Using a pastry blender, food processor or hand mixer cubed butter and vegetable shortening into the dry ingredients until it resembles cornmeal.
After the yeast has become creamy and "bloomed" add to the warm buttermilk and gently stir until combined.
Make a well in the center of the dough and add the buttermilk-yeast mixture.
Gradually work the liquid into the dry ingredients until combined. The dough won't be completely smooth.
Turn the dough out onto a lightly floured non-stick surface. Begin to work the dough, turning and gently kneading just until it comes together and appears smooth.
At this stage, you may divide the dough, in half if desired. Place half into a buttered bowl, and lay a damp towel on top and refrigerate. [Tip: The dough may be stored for up to 1 week in the refrigerator]
Using a floured rolling pin roll the dough to 1/2 inch thickness. Use a 2 or 3 inch biscuit cutter dipped in flour to cut into rounds, reshaping the dough as needed. Do not twist the biscuit cutter use an up and down motion.
Place onto a parchment lined or lightly greased baking sheet, then cover with a damp cloth. Allow to rise in a draft free place for 1 hour. [see cook's note]
Melt remaining 2-4 Tbsp of butter, and brush the tops just before baking.
Preheat the oven to 400°F and bake for 13-15 minutes until golden and cooked through.
Brush tops again with melted butter before serving.
If using Rapid Rise yeast, 1 hour rise time is sufficient. If using plain active dry yeast [long acting] allow the biscuits to rise for 1 1/2 hour.