Season rabbit pieces generously with salt and pepper.
Heat the oil in a large skillet or braising pan over medium-high heat. Brown the rabbit pieces on all sides until lightly golden. Remove and set aside.
In the same pan, add the onion and cook until softened, about 5 minutes. Add garlic and ginger and cook for another 1 minute.
Stir in the gochujang, gochugaru, soy sauce, sugar, mirin, and sesame oil. Cook the mixture for 2 minutes.
Return the rabbit to the pan. Add the stock and the cabbage and bring to a simmer. Cover and cook for 1 hour, until the rabbit is tender and the sauce thickens.
Spread the mozzarella evenly over the top. Cover and cook on low heat until the cheese melts and becomes slightly bubbly. Sprinkle with scallions and sesame seeds.
Serve hot with rice and kimchi. Enjoy!