Whisk eggs in a small bowl. Combine flour and bread crumbs together in a separate bowl.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Dip each cabbage wedge into the whisked eggs; press cabbage wedge into the flour mixture until fully coated. Shake off any excess flour mixture.
Fry the coated cabbage wedges in the hot oil until golden brown, about 10 minutes. Remove from the hot oil with a slotted spoon and drain on a paper towel-lined plate. Sprinkle Parmesan cheese onto each of the fried cabbage wedges.