Soak the boletus in 200 ml of lukewarm water. Rinse the liver, pat dry, remove the tendons and tubes and cut into cubes about 2 cm. Scald the tomatoes with boiling water, peel, quarter, core and cut into narrow strips. Peel onion and garlic and chop finely. Cook the noodles in plenty of salted water until they are firm to the bite.
Drain the mushrooms, collect the water and pour them through a filter bag. Roughly chop the mushrooms. Rinse the sage, pat dry and cut the leaves into strips. Heat the butter and 2 tablespoons of oil in a pan, brown the liver cubes quickly over high heat and remove them. Briefly fry the onion, garlic, sage and mushrooms in the frying fat. Pour in the mushroom water and reduce by about a third over high heat.
Drain the pasta and mix with the olive oil. Mix loosely with the sage and tomato strips and pour into a preheated bowl.
Heat the liver and the juice that has leaked out in the onion sauce and season with salt, pepper and balsamic vinegar. Fold under the pasta and roughly grate the cheese over it.
Tip: Duck or turkey livers are also very fine.
If there is no fresh sage, braise 1/2 teaspoon of dried sage in the sauce and add chopped parsley.