Bring milk and 600 ml water to the boil. Add 3 tablespoons of oil and about 1 teaspoon of salt. Stir in semolina. Continue stirring over low heat for about 5 minutes. Cover and leave to swell for a further 15 minutes on the switched-off hotplate. Stir from time to time
Wash the pods, dab dry, cut diagonally into strips. Clean and wash spring onions and cut them diagonally into rings. Wash thyme, shake dry. Pluck the leaves from the stems and chop them, except for some garnish. Clean and trim the mushrooms, cut large mushrooms smaller if necessary.
Heat 2 tablespoons of oil in a large pan or frying pan. Fry the mushrooms and pods for 4-5 minutes, turning them, and season with salt and pepper. Mix stock, thyme and soy sauce, deglaze mushrooms with it, add 25 g butter and spring onions, simmer for about 1 minute. Mix starch with a little water, thicken simmering broth with it. Season to taste with sugar and possibly salt and pepper
Slice about 20 g of the Parmesan cheese into shavings. Grate the rest of the cheese, add 25 g butter to the semolina and season to taste with salt, pepper and sugar. Arrange polenta and mushroom vegetables, sprinkle with Parmesan shavings and garnish with thyme