Cut cheese crosswise into 3/4-inch pieces, and then lay slices flat and cut in half lengthwise.
Crack eggs into a bowl and beat.
In a second bowl, combine flour and red pepper.
In a third bowl, combine breadcrumbs and parsley.
Dip cheese in beaten eggs. Dredge cheese in flour mixture. Dip cheese back in beaten eggs. Roll cheese in breadcrumb mixture, pressing firmly so that breadcrumbs stick. Set cheese sticks on a wax paper-lined baking sheet and freeze for 30 minutes.
Heat oil to 375° F. Fry cheese sticks until golden brown. Drain on a paper towel-lined plate.