Stir together first 4 ingredients in a medium bowl; cut in butter with a pastry blender or two forks until crumbly. (Mixture will look very dry.) Gently press mixture together with hands, working until blended and smooth (about 2 to 3 minutes).
Shape dough into 2 (4-inch-long) logs. Wrap each log in plastic wrap, and chill 8 hours.
Cut each log into 1/4-inch-thick slices, and place on parchment paper-lined baking sheets. Brush tops with milk.
Bake at 350° for 12 to 15 minutes or until lightly browned.
Parmesan Cheese Bites: Proceed with recipe as directed, omitting fresh basil.
Caryn Nabors, Gadsden, Alabama