In large skillet, heat oil over medium-high heat. Add short ribs in batches and cook until browned. Using tongs, transfer ribs to slow cooker. Add onion to skillet and cook until softened, about 6 minutes. Stir in garlic, ginger, and red-pepper flakes, and cook 1 minute more. Add onion mixture, carrots, broth, hoisin, brown sugar, vinegar, and orange peel to slow cooker. Cover and cook 4 to 5 hours on high or 9 hours on low.
Using a slotted spoon, transfer ribs to serving bowl. Skim fat from sauce and discard. Pour sauce over ribs and garnish with green onion and cilantro.