Preheat the oven to 425° F and line a baking sheet with parchment paper.
In a small bowl, whisk together the buttermilk and the sour cream. Set aside.
Place the flour, baking powder, baking soda, and salt together in a large mixing bowl or into the bowl of a food processor. Whisk or pulse to get the dry ingredients combined. Scatter the butter pieces evenly on top of the flour mixture and cut into the dry ingredients with a pastry cutter or by pulsing several times in the food processor until the mixture resembles coarse crumbs. If using the food processor, transfer the mixture to a large mixing bowl.
Add the buttermilk mixture to the flour mixture and mix until just combined. Turn the dough out to a lightly floured work surface and knead until it just comes together, adding extra flour as needed. Gently mold the dough into a rectangle.
With a rolling pin, roll out the dough into a square (about 12-inches). Using a bench scraper, fold the right third of the dough over the center, then fold the left third over so you end up with a rectangle (about 12 by 4 inches). Fold the top third down over the center, then fold the bottom third up so the whole thing is reduced to a small square (about 4-inches).
Press the square down and roll it out into a square (about 12-inches) and repeat the folding process one more time. Roll out the dough to a square (about 12-inches) and using a lightly floured 4-inch round biscuit cutter, cut six rounds. Transfer the rounds to the prepared baking sheet. Re-roll the dough scraps and cut 2 more 4-inch rounds. Place them on the prepared baking sheet. Place the baking sheet in the refrigerator for 20 minutes. This allows the dough to get cold after handling it.
Remove the biscuits from the fridge, brush the tops with the melted butter and bake for about 15 minutes or until the tops are golden brown. Remove from the oven and cool for a few minutes before serving.