Preheat oven to 350°. Lightly season short ribs with 1/4 tsp. pepper.
Heat oil in a 5- to 6-qt. dutch oven or other heavy ovenproof pot over medium-high heat. Add short ribs and brown on all sides, turning as needed, about 15 minutes total. Transfer short ribs to a plate; set aside. Discard all but 1 tbsp. fat from pot.
Reduce heat to medium and add shallots and coarsely chopped pears to pot; cook, stirring, until shallots are softened and lightly browned, 8 to 10 minutes. Add ginger and garlic and cook, stirring, until fragrant, about 1 minute. Stir in chicken broth, scraping up any browned bits from bottom of pan. Add soy sauce, brown sugar, sesame oil, star anise, and chile flakes.
Increase heat to high and bring mixture to a boil. Return short ribs to pot, cover, and braise in oven 1 hour. Turn meat over and cook until tender but not falling apart, 45 minutes to 1 hour more.
Meanwhile, stir diced pears and rice vinegar together. Chill pear relish, covered, until used.
Uncover meat and continue to oven-braise, turning ribs once or twice, until sauce is reduced by about two-thirds and meat is very tender when pierced, 40 to 45 minutes more. With a slotted spoon, transfer ribs to a plate. Spoon fat from sauce.
Stir cilantro and green onions into diced pear relish and season to taste with salt and pepper. Spoon rice into wide soup plates and set short ribs on top. Spoon a little sauce over meat, then add some pear relish. Serve remaining relish and sauce on the side.
Make ahead: Through step 6, up to 1 day, chilled (with meat in sauce), but don't remove fat. Before serving, spoon off and discard fat from chilled sauce. Reheat on stove, covered, over medium-low heat until meat is hot (an instant-read thermometer inserted in center registers 150°), 20 to 30 minutes.