Bring meat, water and barbecue sauce to boil in Dutch oven or deep large skillet; cover. Simmer on medium-low heat 1 hour.
Add vegetables; stir. Cook covered, 1 hour or until meat and vegetables are tender, stirring occasionally.
Stir in steak sauce; cook 2 minutes.
Sprinkle with chopped fresh thyme leaves just before serving.
Place all ingredients except steak sauce in slow cooker; cover with lid. Cook on low 8 hours (or on high 4 hours). Stir in steak sauce; cook 2 minutes.