Heat a skillet over medium-high heat. Add 1 1/2 teaspoons oil to pan; swirl to coat. Remove sausage from casings. Add sausage to pan; sauté 3 minutes or until browned, stirring to crumble. Remove sausage from pan.
Add 1 tablespoon oil to pan; swirl to coat. Add onion; sauté 3 minutes, stirring occasionally. Add mushrooms; sauté 4 minutes, stirring occasionally. Add garlic; sauté 1 minute, stirring constantly. Stir in sausage, 1/4 teaspoon salt, red pepper flakes, and tomatoes; bring to a simmer. Reduce heat to medium; simmer gently for 15 minutes.
Bring broth and 1 1/2 cups water to a boil in a medium saucepan. Add polenta, stirring well. Reduce heat to medium, and simmer 20 minutes or until thick, stirring occasionally. Stir in remaining 1/4 teaspoon salt, cheeses, and butter. Serve with sausage mixture