1. Melt butter in a large skillet over medium-high heat. Add mushrooms, salt and pepper. Sauté until mushrooms start to give off liquid, about 5 minutes. Add marinara and cook, stirring occasionally, until warmed though, about 3 minutes. Keep warm.
2. Set a rack 3 inches from heat source and preheat broiler to high. Line a broiling pan with foil; lightly oil foil. Arrange polenta on broiling pan and broil until lightly browned, 3 to 4 minutes. Turn and sprinkle with Parmesan. Broil until lightly browned and hot, 3 to 4 minutes longer.
3. Divide polenta among 4 plates. Top with mushroom ragout. Garnish with parsley.