Place half of the mushrooms in a food processor bowl and pulse about 15 times until finely chopped but not pureed, similar to the texture of ground meat. Repeat with the remaining mushrooms and set aside. (To save time, you can also use the food processor to chop the onion, carrot and garlic!)

In a large stockpot over medium-high heat, heat 2 tablespoons of oil. Add the onion and carrot and cook for 5 minutes, stirring occasionally. Add the mushrooms and garlic and cook for 5 minutes, stirring frequently.

While the vegetables are cooking, add the remaining 1 tablespoon oil in a large skillet and heat over medium-high heat. Add 4 slices of polenta to the skillet and cook for 3-4 minutes, until golden; flip and cook for 3-4 minutes more. Remove polenta from the skillet, place it on a shallow serving dish and cover with aluminum foil to keep warm. Repeat with remaining 4 slices of polenta.

To the mushroom mixture, add the tomato paste, oregano, nutmeg, salt, pepper and stir. Continue cooking for another 2-3 minutes, until the vegetables have softened and begin to brown. Add the wine and cook for 1-2 minutes, scraping up any bits from the bottom of the pan while stirring with a wooden spoon. Cook until the wine is nearly all evaporated. Lower the heat to medium.

Meanwhile, in a small, microwave-safe bowl, mix the milk and sugar together and microwave on high for 30-45 seconds, until hot. Slowly stir the milk into the mushroom mixture and simmer for 4 more minutes, until the milk is absorbed. To serve, pour the mushroom veggie sauce over warm polenta slices.