In a medium bowl, combine ribs with soy sauce, ginger, garlic, chiles, and star anise. Cover and chill at least 1 hour and up to 1 day, stirring occasionally.
Preheat oven to 300°. In an 8-qt. pot with ovenproof lid, heat oil over high heat until almost smoking. Lift ribs from marinade (save marinade) and brown on all sides, 4 to 6 minutes total.
Add marinade, broth, and 2 cups water. Cover pot; bring to a boil. Cook in oven until meat is extremely tender, about 3 hours.
Remove bones from ribs and discard. Cut larger rib meat into pieces to make 4 equal portions. Skim excess fat from surface of broth if you like. Return meat to broth. Season to taste with salt and pepper. Add bok choy; let sit, covered, a few minutes to wilt.
Meanwhile, bring a 2-qt. pot of water to a boil. Add noodles and cook until tender, about 3 minutes for fresh and 8 minutes for dried. Drain noodles but don't rinse. Divide evenly among 4 serving bowls. Top with rib pieces and bok choy, dividing evenly, and ladle about 1 1/2 cups broth into each bowl. Serve immediately.
Make ahead: Once ribs are cooked (through step 3), chill overnight and up to 2 days ahead. Remove any solid fat on top. As directed in step 4, remove bones and cut meat into pieces. Reheat meat in broth over medium heat, add bok choy, and proceed with step
Note: Nutritional analysis is per serving; sodium amount varies depending on noodles.