Prep the ribs: Pat short ribs dry and season generously with salt and black pepper. This helps with browning and flavor.
Sear: Heat oil in a heavy pot or Dutch oven over medium-high.
Sear ribs on all sides until deeply browned, about 8–10 minutes total. Work in batches so they brown, not steam.
Aromatics: Reduce heat to medium. Add onion, garlic, and ginger.
Sauté 2–3 minutes until fragrant, scraping up browned bits.
Build the sauce: Stir in gochujang, gochugaru, soy sauce, brown sugar, rice vinegar, sesame oil, and beef broth. Add carrot, grated pear, green onions, and chilies if using. Return ribs and any juices to the pot, nestling them into the liquid.
Braise: Bring to a gentle simmer, cover, and cook on low for 2.5–3 hours, turning ribs once or twice, until the meat is tender and pulls away from the bone.
Reduce the sauce: Transfer ribs to a plate.
Skim excess fat from the surface. If you want a thicker sauce, simmer uncovered to reduce or whisk cornstarch with 2 tablespoons water, then stir into the pot and simmer 2–3 minutes.
Finish and serve: Return ribs to the pot to glaze. Taste and adjust seasoning—add a splash of vinegar for brightness or a pinch of sugar for balance.
Garnish with sesame seeds and green onions. Serve over rice or potatoes.