Cut cheese crosswise into 3/4-inch slices. Lay slices flat and cut in half lengthwise.
Combine flour and cayenne pepper; stir well. Combine bread crumbs and parsley in another bowl; stir well. Dip cheese sticks in beaten eggs. Dredge in flour mixture. Dip coated cheese in egg again; dredge in bread crumb mixture, pressing firmly so that crumbs adhere. Place cheese sticks on a wax paper-lined baking sheet and freeze at least 30 minutes.
Heat 2 inches of oil in a Dutch oven to 375°. Fry cheese sticks until golden. Drain on paper towels. Serve immediately with marinara sauce, if desired.