Position a rack in the center of the oven and preheat to 450 degrees F. Line a baking sheet with parchment paper.
Whisk the flour with the sugar, baking powder, lemon zest, black pepper, and salt in a large bowl.
Cut butter into tablspoon size pieces. Rub in 2 tablespoons of the butter with your fingers until no visible pieces remain. Rub in the remaining 4 tablespoons of butter just until it is in even, pea-size pieces.
Scatter grated and diced cheese over the top and toss with a rubber spatula. Using a wooden spoon, stir in the milk to make a loose dough.
Turn dough onto a lightly floured surface and pat into a rectangle about 1/2 inch thick. Fold dough into thirds, like a business letter, and pat lightly into an 8x5-inch rectangle - about 3/4 inch thick.
Using a 2-3 inch round biscuit cutter, cut 6 biscuits and place on baking sheet. Press dough scraps together and cut 2 more biscuits.
Bake until tops are lightly browned, about 15 minutes. Cool slightly on a wire rack and serve warm.