Cook parsnips, covered, in a very small amount of boiling water until almost done.
Drain well; squeeze parsnips between paper towels to remove excess moisture.
Combine parsnips, green onions, egg, flour, salt, and pepper, stirring well.
Drop 1/4 cup parsnip mixture at a time into 1/8 inch hot oil; press into 3 inch rounds with the back of a fork.
Fry until golden brown, turning once.