Prepare polenta according to package directions, using 1/2 teaspoon salt. Set aside, and keep warm.
Remove brown gills from the undersides of mushrooms, using a spoon; discard gills. Slice mushroom caps; set aside.
Heat oil in a large Dutch oven. Add onion; cook over medium heat, stirring constantly, 3 minutes or until softened. Add remaining 1/2 teaspoon salt, sliced mushrooms, and pepper. Cook 5 minutes or until mushrooms are tender, stirring frequently.
Sprinkle flour over mushrooms, and cook 30 seconds, stirring constantly. Add wine and broth; bring to a boil. Reduce heat, and simmer, uncovered, 2 minutes or until thickened, stirring constantly. Stir in parsley and rosemary. Serve immediately over prepared polenta. Sprinkle 1 tablespoon cheese over each serving.