Combine rice wine, black pepper, and ginger in a shallow dish. Toss in chicken to coat. Marinate for 15 minutes.
Mix gochujang, soy sauce, corn syrup, sugar, garlic, chili powder, and sesame oil together in a bowl for the sauce.
Heat vegetable oil in a wok over medium-high heat. Add potatoes and carrots; cook and stir until slightly tender, about 5 minutes. Pour in water. Add the chicken and onion; stir to combine. Add the sauce, stir, and bring stew to a boil. Boil until chicken is no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Stir sesame leaves into the stew. Cook until wilted, about 1 minute more.