Stir together warm water, yeast, and 1 teaspoon sugar in a small bowl. Let sit 5 minutes.
Stir together flour, 1/4 cup sugar, and salt in a large bowl.
Cut butter and shortening into the flour mixture with a pastry blender or 2 forks until crumbly.
Add yeast mixture and buttermilk to flour mixture. Stir together just until dry ingredients are moistened.
Cover bowl with plastic wrap and refrigerate for 2 hours up to 5 days.
Preheat oven to 400 degrees.
Turn dough out onto a floured surface. Knead 3 or 4 times. If too sticky sprinkle some more flour on top as you knead it.
Roll dough into a 3/4-inch thick circle. Fold dough in half and roll out. Repeat. Roll dough into a 3/4-inch circle.
Cut biscuits out with a 2 1/2-inch or 3-inch biscuit cutter.
Place biscuits in a greased 10 or 12-inch cast iron pan so that their sides touch. Or you can use a baking sheet lined with parchment paper. Brush biscuits with half of the melted butter.
Bake 15 to 20 minutes or until golden brown.
Brush with remaining melted butter and serve.
Notes
Be sure the warm water is no hotter than 110 degrees ofr it may kill the yeast.