Wash the arugula and spin dry. Clean the oyster mushrooms and fry them in 2 tablespoons of hot oil. Season with salt and pepper, remove from the pan and keep warm. Reduce vinegar with 1 tablespoon of sugar to half.
Gradually fold in 3 tablespoons of oil. Cut the beef fillet into 8 slices. Season with salt and pepper and sprinkle with some sugar. Heat 1 tablespoon in the pan. Fry the fillets on each side for about 2 minutes.
Fry over medium heat for about 4 minutes. Arrange fillets, oyster mushrooms and rocket on plates as a stack. Finely slice Parmesan cheese with a peeler. Serve with vinaigrette. Garnish with lemon wedges and cherry tomatoes.