Coat a large nonstick skillet with cooking spray; add oil. Place over medium-high heat until hot. Add onion and garlic; cook, stirring constantly, until onion is tender. Stir in thyme and next 4 ingredients; cook 30 seconds. Remove from heat, and set aside.
Combine water and 1 cup vinegar in a large Dutch oven; bring to a boil. Add cabbage, and cook 10 seconds, stirring constantly; drain. Add cabbage, 2 tablespoons vinegar, and chicken broth to onion mixture; bring to a boil. Cover, reduce heat, and simmer 15 minutes or until cabbage is crisp-tender. Remove and discard bay leaves.