Season beef with salt, pepper, and thyme. Roll it in the flour.
Heat the oil in a large skillet over medium-high heat. When hot, add beef (in batches if necessary to prevent crowding) and cook until browned all over, 4 to 5 minutes. Remove to a slow cooker.
Discard all but 2 tablespoons of the fat in the skillet. Add onions and celery, and cook until soft, about 5 minutes. Chop 1/2 cup of the carrots and add them to the skillet along with the garlic. Cook 2 minutes, and then transfer to a slow cooker.
Add the remaining carrots, potatoes, tomatoes, broth or wine, Worcestershire sauce, and bay leaves to the slow cooker. Cover and cook on high for 4 to 5 hours or on low for 8 hours. Remove bay leaves before serving.
Tip: To skip the slow cooker, brown the seasoned beef in a Dutch oven or large soup pot and transfer it to a plate. Sauté the onions, celery, carrots, and garlic in the pot, and then add the remaining ingredients, bringing them to a boil over high heat. Reduce heat to medium-low, cover, and cook until the meat is tender, 1 1/2 to 2 hours.