In a wide, tall saucepan, bring the milk, vegetable stock and salt to the boil. Stir in the semolina and let it simmer uncovered over low heat for about 25 minutes to a porridge. Stir frequently. If the porridge is too soft, stir in some more semolina, it will be too firm and add a little hot water.
Finally stir in the egg and 1 tablespoon butter and season with nutmeg, pepper and a little salt. Oil a baking sheet and spread the polenta evenly thick on it. Then cool for at least an hour and allow to set.
In the meantime, wash the tomatoes, remove the stalks and cut into slices. Drain the mozzarella well and also cut into slices. Wash and finely chop the basil leaves.
Clean the mushrooms and cut into thin slices. Melt 1 1/2 tablespoon butter in a saucepan and stir-fry the mushrooms over a medium heat until they have given off all the liquid.
Grease a baking dish. Preheat the oven to 200 °. Cut the solidified polenta into equal-sized squares of about 6 cm, then divide them into triangles.
Layer the polenta triangles, the mozzarella slices, the tomatoes and the mushrooms alternately in the baking dish. Sprinkle with the parmesan and top with the remaining butter in small flakes. Then bake the polenta in the oven for 15 minutes until it is golden yellow. Sprinkle with the basil before serving.
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