Spray 6- to 7-quart slow cooker with cooking spray. In cooker, place carrots, onion and garlic. Sprinkle beef ribs with salt and pepper; place on vegetables. Top with mushrooms, parsley and bay leaves.
In medium bowl, beat wine and tomato paste with wire whisk until blended; pour over rib mixture.
Cover; cook on Low heat setting 8 to 10 hours.
Transfer ribs and vegetables to platter, with slotted spoon; discard parsley and bay leaves. Keep warm. Spoon fat from top of cooking liquid.
In small bowl, stir water and flour until well blended; stir into cooking liquid. Increase heat setting to High. Cover; cook 15 to 20 minutes longer or until gravy is thickened. Serve gravy with ribs and vegetables.