1. Place first 7 ingredients in a 6-qt. slow cooker.
2. Toss oxtails with salt and pepper. Sprinkle with flour; toss to coat. Cook oxtails, in 2 batches, in hot oil in a large skillet over medium heat 3 to 4 minutes on each side or until well browned. Transfer oxtails to slow cooker, reserving drippings in skillet.
3. Add wine to reserved drippings in skillet; cook 1 minute, stirring to loosen brown bits from bottom of skillet. Whisk in tomato paste; cook, stirring often, 2 minutes. Pour over oxtails.
4. Cover and cook on LOW 5 to 6 hours. Add mushrooms; cook 1 more hour.
5. Remove oxtails and vegetables using a slotted spoon. Discard bay leaves and herbs. Skim fat from juices in slow cooker; season with salt and pepper. Serve immediately over oxtails, vegetables, and hot cooked rice.