Trim fat from beef. Cut the beef into 1-inch cubes. Combine beef and 3 tablespoons flour in a large zip-top plastic bag. Seal bag, and shake well to coat. Heat oil in a large Dutch oven over medium heat. Add beef, and cook 5 minutes, browning on all sides. Add 1 1/2 cups water and next 6 ingredients (water through broth); bring to a boil. Cover, reduce heat to low, and simmer 1 hour.
Combine cold water and 1 tablespoon flour in a small bowl; stir well. Add flour mixture, eggplant, potatoes, chestnuts, and tomatoes to beef mixture; bring to a boil. Cover; reduce heat to medium-low. Simmer 30 minutes or until vegetables are tender and stew is thick. Garnish with thyme sprigs, if desired.