Heat 1 1/2 teaspoons oil in a large saucepan over medium-high heat. Add the mushrooms; sauté 5 minutes or until golden. Remove mushrooms from pan.
Heat 1 1/2 teaspoons oil in pan over medium-high heat. Add carrot and next 4 ingredients (carrot through garlic); sauté 5 minutes. Add wine, and cook until reduced to 1/4 cup (about 1 minute). Add mushrooms, broth, turkey, chopped thyme, salt, and pepper. Bring to a boil, reduce heat, and simmer 15 minutes or until the vegetables are tender. Garnish with thyme sprigs, if desired.