Boil 1.5 liters of water in a large saucepan with a thick bottom, add salt and, stirring constantly in one direction, pour in the corn grits in a thin stream.
Simmer over low heat, stirring constantly, for 30 minutes, until the polenta begins to pull away from the sides of the pan. Pour a few tablespoons of olive oil, stir and spread the polenta in an even layer in the form of a circle or rectangle on a baking sheet covered with parchment. Let cool.
Meanwhile, put the mushrooms in boiling salted water, cook for 3-4 minutes. Throw in a colander, dry. Peel and mince the garlic. Saute mushrooms with garlic in 3-4 tbsp. l. olive oil. Put the tomato sauce on the polenta, then the fried mushrooms, capers, halved olives and anchovies.
Drizzle with olive oil, salt, pepper and bake in the oven at 200ºС for 10-12 minutes.