Heat oil in a large nonstick skillet over medium heat. Add onion and garlic; sauté 5 minutes or until tender. Add mushrooms, thyme, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Cook over medium-high heat 8 minutes or until mushrooms are tender, stirring frequently. Combine cornstarch, broth, sherry, and Worcestershire sauce; stir well. Add cornstarch mixture to mushroom mixture; bring to a boil over medium-high heat. Cook 2 minutes or until mixture is slightly thick, stirring frequently.
Bring water to a boil in a large saucepan. Stir in polenta; reduce heat to medium, and cook 3 to 5 minutes or until thick, stirring constantly. Add spinach, yogurt-based spread, cheese, and remaining 1/4 teaspoon each of salt and pepper; stir well to combine. Remove from heat; let stand 3 minutes or until spinach wilts, stirring often. Spoon polenta onto plates and top with mushroom mixture.