1. Pat ribs dry with paper towels.
2. In a large skillet, heat oil over medium heat. Add as many ribs as will fit in pan without touching. Cook them in batches, turning occasionally, until nicely browned on all sides, about 20 minutes total. Place browned ribs in a large slow cooker. Sprinkle with salt and pepper to taste.
3. Spoon off all but 2 tablespoons of the fat from skillet. Add onions and cook for 10 minutes or until tender. Stir in tomato puree, garlic, tomato paste, herbes de Provence and allspice. Bring sauce to a simmer, stirring well.
4. Scrape contents of skillet into slow cooker. Cover and cook on LOW for 8 hours or until meat is tender and coming away from the bones.
5. When ribs are almost ready, stir in mushrooms. Cover and cook for 30 minutes more.
6. Discard any loose bones and skim off fat. Sprinkle with parsley and serve hot.