Place onions in large saucepan or bowl. Add both eggs and blend together, using hand mixer, until smooth. Add beef and breadcrumbs, mix with a wooden spoon then blend well with mixer. Add all other ingredients and mix well.
Scoop out a medium handful of the mixture and roll into a ball. Pat down into a disc shape. Heat oil in a fry pan, or lightly oil barbecue plate then cook patties on both sides until cooked to your preference.
Serve in a plain roll, with cheese, thinly sliced onion, tomato, beetroot and lettuce - or any salad combination you like.