1. Preheat oven to 425°.
2. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, sugar, baking powder, and salt in a medium bowl, stirring with a whisk. Cut in butter with a pastry blender or 2 knives until mixture resembles coarse meal. Stir in basil and cheese. Combine milk and egg in a small bowl, stirring with a whisk. Add milk mixture to flour mixture; stir just until moist. Turn dough out onto a floured surface; pat to 1-inch-thick circle. Cut with a 2-inch biscuit cutter into 12 biscuits. Place biscuits on a baking sheet coated with cooking spray. Bake at 425° for 15 minutes. Remove from oven, and cool.