Whisk the flour, baking powder, and salt together in a mixing bowl.
Add the butter and use a pastry blender or fork to combine it with the flour until the mixture is coarse and sandy.
Use your fingers to rub in any remaining larger lumps of butter. Place the bowl of flour in the freezer for 30 minutes.
Preheat the oven to 450ºF (230ºC).
Line a baking sheet with parchment paper and have a 2½ inch (6 mm) round biscuit cutter ready.
Remove the flour mixture from the freezer and add the grated cheese.
Stir everything together with a fork to combine.
Use the fork to make a well in the middle of the flour-cheese mixture.
Pour in the milk.
Stir everything together with the fork until no dry bits of flour remain on the bottom of the bowl.
Turn the dough out onto a floured work surface.
Sprinkle a little flour on top of the dough. Working quickly so the butter doesn't warm up, pat the dough out to a thickness of 1 inch (2½ mm) with your hands. Add a little more flour if the dough is sticking.
Cut the dough into as many round biscuits as you can (probably about seven). Gather the leftover scraps and quickly pat the dough out again. Cut more biscuits. Repeat this process until all of the dough is gone. Depending on how thick you’ve patted the dough, you should end up with 10 to 12 biscuits.
Place the biscuits on the prepared baking sheet and brush the top of each with milk.
Bake the biscuits for 15 to 17 minutes, or until golden.
Remove them from the oven and let the pan cool on a wire rack for 10 minutes before serving.
Notes
Do not use pre-shredded cheese. Bagged, shredded cheese generally has a light coating of cornstarch to prevent it clumping and sticking together in the bag. It doesn't melt as well as cheese you grate by hand yourself.