1. Make the short ribs: Preheat oven to 325 degrees. Heat oil over medium-high heat in a large Dutch oven. Season ribs with salt and pepper, and cook in batches until golden brown, 3 to 4 minutes per side. Transfer ribs to a plate, leaving drippings in pot.

2. Reduce heat to medium. Add garlic, shallots, onion, and chiles, and cook, stirring frequently, until golden, about 10 minutes. Return meat to pot and add scallions, pear, star anise, soy sauce, wine, vinegar, honey, and ginger. Add water to cover by 1 inch, and bring to a simmer. Cover, and transfer to oven. Cook until ribs are fork tender, about 3 hours. (Ribs in liquid can be cooled, covered, and refrigerated up to 2 days. Bring to room temperature, then proceed with step 5.)

3. Make the celery root puree: Bring celery root and cream to a boil in a medium saucepan. Reduce heat and simmer until celery root is tender, about 30 minutes. Strain celery root, reserving cream. Puree celery root with 2 cups of reserved cream in a blender until smooth. Season with salt and pepper. (Celery root puree can be made up to 1 day ahead; reheat over low heat.)

4. Make the celery-pear salad: Mix celery, pear, scallion, and jalapeno in a small bowl. Toss with oil and lime juice, and season with salt and pepper.

5. Transfer ribs to a plate and strain sauce through a fine sieve. Skim fat from top, and discard. Return sauce to pot, and cook over medium heat until sauce just coats the back of a spoon, about 10 minutes. Add ribs to sauce, and cook, basting often, until ribs are hot and sauce coats meat, about 5 minutes. Serve ribs on top of celery root puree, and drizzle with sauce. Top with pear salad.