Heat oil in a large Dutch oven over medium high heat. Add shanks; brown on all sides, about 15 minutes. Transfer to a large bowl.
Add onions, carrots and celery to Dutch oven. Sauté until vegetables are brown, about 8 minutes.
Return shanks to the Dutch oven. Pour wine over the meat and boil until all liquid evaporates, about 5 minutes. Add garlic and tomato paste. Cook 1 minute. Add broth, water, rosemary, thyme and parsley. Cover; bake in oven until shanks are tender, 2 to 2 1/2hours.
Transfer the shanks to the bowl. Boil cooking liquid until thickened to sauce consistency, about 35 minutes. Season with salt and pepper. Discard rosemary, thyme and parsley. Return shanks to sauce; heat through and serve.
Notes
If you are preparing this recipe as GLUTEN-FREE, just be sure to use brands of tomato paste and chicken broth that are known to be GF.