Preheat oven to 450°F/230°C.
In a small bowl, toss together cheese, chives, and bacon with 1 tablespoon flour. Set aside.
In a separate bowl whisk together flour, baking powder, and salt. Use a pastry cutter or two forks to cut in butter (or see note below about using a box grater with frozen butter).
Add milk and stir just enough to bring the ingredients together. This should make a soft, sticky dough. If the dough seems too dry, continue adding a splash of milk or cream to the bowl until the dough becomes sticky and forms a ball. Don't worry -- the dough will be less sticky and will come together nicely when it's kneaded on the flour surface and that extra flour is incorporated.
Gently fold in the cheese mixture.
Turn dough onto a floured surface and knead for about 1 minute.
Pat or roll out dough to ¾-inch thickness.
Cut into rounds (I used a 2 ½ inch round biscuit cutter, but a juice glass will also work!).
For crisp biscuits, place far apart on an ungreased baking sheet. For fluffier biscuits, place them close together (touching) on an ungreased baking sheet.
Bake for 12-15 minutes or until golden brown on top.