Sear the beef cheeks in half the oil in a large heavy-based saucepan over a high heat, until browned. Set aside. Add the carrots, carrots and remaining oil, cook until aromatic, then set aside in a second dish.
Return the beef cheeks to the saucepan and cover with cold water. Bring to a simmer and cook for 15 minutes, skimming the floating sediment while it bubbles. Meanwhile, combine the pear, onion, kimchi, soy, sugar, honey, vinegar, sesame oil and ginger in a blender and puree until smooth.
Add the sauce to the pan along with the carrot mixture, jujube and nuts, then fit the lid and simmer gently for 2½ hours, until tender. Serve with rice, green shallots and sesame seeds.