Grate vegetables by hand or with grating disk of a food processor. In a bowl, mix together all ingredients except the butter or oil. Mixture should be fairly loose but not liquid; add a little more flour or bread crumbs if necessary.
Put butter or oil in a large skillet and turn heat to medium-high. When pan is hot, put large spoonfuls of batter in pan. Cook, turning once, until nicely browned on both sides, 10 to 15 minutes total. Serve hot or at room temperature.