Preheat the oven to 425 degrees F.
In a large bowl, whisk together the flour, baking powder, baking soda, salt and 3 tablespoons of the sugar.
In a small bowl, combine the warm water with the yeast and the remaining 2 tablespoons sugar; stir until the yeast is dissolved. Let stand until bubbles appear, 2 to 3 minutes.
Using your hands, mix the 1 cup cold butter into the flour, breaking the butter into small pebbles, until the mixture resembles coarse meal. Make a well in the center and add the buttermilk and the yeast mixture. Gently fold the flour into the wet ingredients. Keep mixing until a ball starts to form, then gently knead, 12 to 15 times, to create a smooth dough. Cover with a cloth or plastic wrap and let rise in a warm place for approximately 1 hour.
Transfer the dough to a lightly floured work surface and press out to 1- to 1 1/2-inches thick. Fold the dough in half, press again to 1- to 1 1/2-inches thick, and then fold again. Cut the dough using a 2- to 3-inch round biscuit cutter, depending personal preference. Brush the bottom of a cast-iron skillet with some of the melted butter. Place the biscuits in the skillet; brush the tops with melted butter.
Bake until golden brown, 18 to 22 minutes, depending on size. Brush again with melted butter and serve immediately.