"Grate" cooked parsnips in a food processor or potato ricer, but leave small lumps. Don't make it too smooth.
In a large mixing bowl, fold together parsnips, eggs, flour, and all seasonings through sugar. Mix until well blended. Cover and refrigerate for 1 hour, or until very cold.
Shape into 3"x1/2" patties.
Heat oil (or butter) in skillet on low to medium heat. (Not too high, or the outside will brown too quickly, and the egg in the middle will not cook.) Cook croquettes approximately 8 minutes on each side. Turn carefully to prevent croquettes from falling apart. When both sides are golden brown and center is firm, remove from heat.
Enjoy as a side dish.
Or, place in casserole dish and cover with your favorite cream sauce leaving the tops exposed. Cook in 350 degree oven until sauce is bubbly. Sprinkle mozarella cheese on top of each croquette and continue to cook until cheese is melted and slightly brown. Serve as a vegetarian main dish.