Preheat oven to 400°F. Lightly sprinkle heavy large baking sheet with flour. Combine 3 cups flour, 1/2 cup cheese, sugar, baking powder, salt, and pepper in large bowl; whisk until well blended. Add butter and rub in with fingertips until coarse meal forms. Mix in parsley. Gradually add 1 cup milk, tossing with fork until moist clumps form and adding more milk by tablespoonfuls if mixture is dry. Gather dough into ball. Press out on lightly floured work surface to 8-inch round, about 1 inch thick. Using 2-inch-diameter cutter, cut out biscuits. Repeat, gathering and pressing out dough and cutting biscuits until all dough is used. Arrange biscuits on prepared baking sheet. Sprinkle with remaining 1/4 cup cheese.
Bake until biscuits are puffed and light golden and tester inserted into centers comes out clean, about 15 minutes. Transfer biscuits to towel-lined basket and serve warm.
Bon Appétit, December 2003