Bring the milk to a boil with 30 grams of butter, pour the semolina in a thin stream, stirring for 2-3 minutes. Remove from heat, salt and pepper. Divide the egg into yolks and whites. Stir the yolk into the semolina. Beat the protein until stiff peaks and add to the semolina. Boil salted water in a large saucepan. Using two spoons, form dumplings from semolina mass and dip them in boiling water. Cook on low heat for 15 minutes. Remove the dumplings with a skimmer and place them on a sheet covered with parchment.

Cut the onion into small pieces, cut the mushrooms into slices. Melt 20 grams of butter in a saucepan and saute onions with mushrooms for 5 minutes. Pour the broth, bring to a boil and cook for 10 minutes. Add salt and pepper to taste. sprinkle dumplings on a baking sheet with grated cheese. Bake the dumplings under the grill in the oven for 5 minutes and put them in broth. Sprinkle with green onions and serve.