Preheat oven to 425°F. Line two baking sheets with parchment paper or silicone mats. Set aside.
In a large bowl, sift or whisk together the flour, baking powder and salt.
Grate the frozen butter into the flour. Using a wooden spoon or your finger tips, toss the butter and flour mixture so that the little butter pieces are coated in flour and dispersed throughout. (Tip: if you don’t want to grate the butter, you can just cut in diced, chilled butter with a pastry cutter until the mixture resembles coarse meal).
Gradually add the buttermilk to the flour mixture; stir or knead just until a soft dough comes together. If you still see dry pockets of flour, gradually add a little bit more buttermilk, one splash at a time, until the dough holds together. Fold in the grated cheese.
Scoop about ¼-cup to ⅓ cup of dough and drop onto the prepared baking sheets. I use an ice cream scoop for this step, which keeps the biscuits the same shape and size. If the dough is sticking to your scoop, spritz the scoop lightly with nonstick spray.
If the dough becomes warm while you mix and scoop (or if your kitchen is warm), pop the trays of biscuit dough back in the refrigerator or freezer for about 5-10 minutes to chill before baking. You want the dough as cold as possible when it goes into the oven so that the biscuits rise high and don't spread too much.
Bake for about 15 minutes, or until golden brown on top. Brush the tops of the biscuits with melted butter as soon as they come out of the oven. Serve warm.