Heat oil in medium Dutch oven over medium heat. Add onion and garlic; cook, stirring, until onion is softened, about 5 minutes.
Reduce heat to medium. Add all remaining ingredients except mushrooms and thyme leaves to Dutch oven; bring to boil. Reduce heat and simmer, covered, 1 hour.
Add mushrooms to pot and simmer, covered, until meat is fork-tender, about 1 hour longer. Remove and discard thyme sprigs. Serve sprinkled with thyme leaves.
PER SERVING: (about 1 cup stew): 327 Cal, 8 g Total Fat, 2 g Sat Fat, 0 g Trans Fat, 56 mg Chol, 521 mg Sod, 18 g Carb, 5 g Sugar, 3 g Fib, 31 g Prot, 35 mg Calc.
Reprinted with permission from Weight Watchers One Pot Cookbook, copyright (c) 2011. Published by Wiley.