1. To prepare medley, heat a large skillet over medium-high heat. Add oil to pan; swirl to coat. Add mushrooms, garlic, onion, and thyme; sauté 8 minutes or until lightly browned, stirring frequently. Add wine and vinegar; cook 2 minutes or until liquid is reduced by half. Add broth, pepper, 1/4 teaspoon salt, olives, and chickpeas; bring to a boil. Reduce heat to medium; simmer 6 minutes or until slightly thickened.
2. To prepare polenta, bring 3 cups water and 1/4 teaspoon salt to a boil in a medium, heavy saucepan over medium-high heat. Gradually add polenta, stirring constantly with a whisk. Reduce heat to low; cook 30 minutes or until thick and creamy, stirring frequently. Stir in 1 ounce cheese.
3. Divide polenta evenly among 6 shallow bowls. Top evenly with mushroom mixture. Sprinkle evenly with remaining 1 ounce cheese and parsley.