Preheat oven to 350F. Lightly grease baking sheets; set aside. In a large bowl, combine shredded cheese and butter; let stand until room temperature (about 1 hour). Beat with an electric mixer until well mixed. Stir in flour, cornmeal, salt, cayenne pepper, and nutmeg. Divide dough in half.
On a lightly floured surface, roll each dough half into a 12x4-inch rectangle. Using a sharp knife, slice dough into 4x1/2-inch pieces.
Place dough pieces 1/2 inch apart on prepared baking sheets. Bake about 15 minutes or until bottoms are lightly browned. Transfer to a wire rack; cool. Makes 48 crackers.