Heat oven to 425 degrees. In a large bowl, thoroughly combine flour, salt, baking powder, cream of tartar, sugar, and cayenne.
Cut butter into pieces, and work it in with your fingers until mixture is coarse and crumbly. Stir in cheese.
Make a well in center of flour mixture, pour in milk, and stir with a fork just until dough comes together. Do not overmix. Turn onto a lightly floured surface, and knead gently 10 to 12 times.
Pat dough into a circle about 1/2 inch thick. Cut out biscuits using a floured 2-inch-round cutter. Do not twist cutter. Transfer biscuits to a lightly buttered baking sheet, and bake until brown, 12 to 15 minutes. Serve hot.