Mix the vegetables very thoroughly with the ground beef, egg, salt and pepper.
Form into patties and brown on both sides over medium high heat.
Cook over lower heat for about 10 minutes in total, or until they are cooked through.
They are somewhat delicate, so treat them gently.
They should be turned once during cooking.
Spoon off excess fat, but do not clean the pan.
Stir together the cornstarch, water or broth, paprika and Worcestershire sauce, and pour it into the pan as soon as the patties have been removed.
It will boil up and thicken rapidly.
Pour it over the beef patties to serve.
(If there is not a great deal of fat in the pan, the gravy can be made while the patties are still in the pan.) If your meat is very fresh, half of the mixture can be kept well covered in the fridge and cooked the next day, but no later than that.