Preheat oven to 450 degrees.
Slice the polenta into 1/2-inch slices or 1/2-inch thick rounds.
Brush both sides lightly with olive oil and place on a rimmed baking sheet covered with parchment paper. Roast until golden brown and warmed through, about 25 minutes.
Meanwhile, in a large skillet, heat the oil over medium heat and add mushrooms. Stir often until tender and slightly browned, about 12 minutes.
Add cut shallots, vinegar, salt, and red pepper. Sauté for about 5 minutes. Stir in parsley.
Place a teaspoon of tomato sauce on each slice of roasted polenta.
Divide mushroom mixture and spoon over the tomato sauce.
Top with cheese and continue to roast in the oven until cheese is melted, about 5 minutes.