Preheat oven to 475°F.
In a small bowl, toss together cheese, chives, and bacon with 1 tablespoon of flour. Cover and transfer to the refrigerator.
Place remaining 2 ½ cups flour in a large mixing bowl. Using the larger holes on a box grater, grate the stick of butter into the flour. Use your fingers to coat all of the butter with flour, and then work the butter into the flour with your finger tips for about 2 minutes. Chill in the freezer for 10 minutes.
Make a well in the center of the flour mixture. Add the buttermilk, and stir with a wooden spoon (or with your hands) just until a shaggy dough comes together. Gently fold in the cheese, chive, and bacon mixture. Add a very small amount of extra buttermilk, if necessary, to bring the dough together (it should still be a bit crumbly -- not too wet). The dough will continue to come together on the countertop.
Turn the dough onto a well-floured work surface. Fold the dough over onto itself 6-8 times, just until it comes together. Pat the dough into a rectangle that’s about ¾ inch thick.
Use a 2 ¼-inch round biscuit cutter to punch out the biscuits (do not twist the cutter). Arrange the biscuits with sides touching in a 10-inch cast iron skillet, in a round cake pan, or on a parchment-lined baking sheet. Re-roll the scraps and cut out additional biscuits until all the dough is used.
If time allows, place the biscuits back in the freezer for 10-15 minutes to chill again before baking.
Bake for 13-18 minutes, or until golden brown. Brush the hot biscuits with the melted butter. Serve warm.