Step 1Heat oil in large stewpot over medium high heat. Season ribs with salt and pepper to taste. When oil is hot, sear ribs in batches. Set aside.
Step 2Keep about 2 tablespoons fat in pot. Add onions and garlic. Stir until mixed. Cook, stirring often, until hot and fragrant, about 5 minutes. Add celery, celery root, rutabaga, potato, bay leaf, thyme, broth, water and tomatoes with juice. Bring to boil, then reduce heat and simmer, partially covered, until meat is falling off bones, about 2 1/2 hours.
Step 3Use tongs to transfer ribs to plate. When cool enough to handle, remove meat from ribs, trim away fat and cartilage (there will be more waste than meat). Use hands to shred meat. Stir into soup. Cool, then refrigerate overnight or up to 3 days. Skim and discard solid fat. (Can be frozen up to 1 month.) Reheat over medium high heat, stirring often. Taste and adjust seasoning. Simmer, uncovered, to thicken as desired. Remove bay leaf. Serve hot in warm soup bowls.