Combine 1 1/2 cups broth and 1 cup water in a medium saucepan; bring to a boil over high heat. Gradually add polenta, stirring with a whisk. Reduce heat to low; cook 5 minutes or until very thick, stirring constantly. Stir in Parmesan cheese. Spoon polenta into an 8-inch square baking dish coated with cooking spray, spreading evenly. Press plastic wrap onto surface of polenta; chill 2 hours or until firm.
. Cut polenta into 4 squares. Cut each square in half diagonally to form triangles.
. Heat 1 teaspoon oil in a large nonstick skillet over medium-high heat. Add half of polenta triangles; cook 4 minutes on each side or until golden. Remove from pan; keep warm. Repeat procedure with 1 teaspoon oil and remaining polenta.
. Heat remaining 1/2 teaspoon oil in pan over medium-high heat. Add mushrooms and next 3 ingredients; sauté 3 minutes or until golden brown. Combine remaining 1 1/2 cups broth, wine, and cornstarch; stir until well blended. Add broth mixture, thyme, and parsley to mushroom mixture; bring to a boil, and cook 7 minutes or until slightly thick, stirring constantly. Spoon sauce over polenta; sprinkle with goat cheese. Garnish with thyme sprigs, if desired.