In a mixing bowl, combine onions, mayonnaise, lime juice, garlic, and cayenne pepper.
Stir in salmon, egg and cubed bread, make sure all are combined well.
Let sit for 5 minutes.
On a plate, put the breadcrumbs.
Make 9 even balls of salmon mixture and arrange them on another plate. Then take each ball, roll in the breadcrumbs and flatten to about ½-inch patties.
Place on a griddle that has been heated to medium heat with the olive oil on it.
Fry for 4 minutes, then turn each patty and cook an additional 4 minutes.
After both sides are browned, turn patties again and add half the butter to the griddle in tiny portions, so all the patties have butter on them. Cook for an additional 2 minutes, turn and repeat, so both sides are golden brown.