To prepare beef patties: Half an hour before cooking, combine the beef and pine nuts; divide the mixture into four equal portions and shape into round, 2cm-thick patties. Refrigerate for 30 minutes.
To cook: Heat a little olive oil in the pan over medium heat. When oil is hot, add the meat patties and cook on both sides to the preferred doneness. Sprinkle both sides with salt and freshly-ground black pepper to taste and remove the pan.
Melt butter in a frying pan over low heat and fry the mushrooms until browned.
To assemble: Preheat the oven to 200 .Place a beef patty on a bread slice and top with a slice of cheese and a few slices of mushroom. Gratinate on the top deck of the hot oven to melt the cheese - place the remaining bread slices in the oven to toast them lightly at the same time. Top with another slice of bread and serve immediately.