Melt 2 tbsp butter in skillet over medium heat. Add sliced onions and saute until tender. Add sugar, and continue to saute until they are starting to carmelize (turn brown). Remove from pan and keep warm.
In the meantime, gently mix together the ground beef, breadcrumbs, egg, milk, allspice, ginger, grated onion, salt and pepper. Form into 4 patties.
Melt 2 tbsp butter in skillet over medium heat. Add patties and fry until brown. Flip the patties and brown the other side. Add the water, cover, and simmer for 15 - 20 minutes until cooked through.
Serve, topped with the onions and, if you like, the Swedish Cream Sauce, potatoes and pickles.