In a large bowl, combine the gochujang, soy sauce, sugar, minced garlic, and sesame oil to make the sauce. Mix well until all the ingredients are combined.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced onion, julienned carrot, and bell pepper to the skillet. Stir-fry for about 2-3 minutes until the vegetables start to soften.
Add the sliced octopus to the skillet and continue to stir-fry for another 4-5 minutes until the octopus is cooked through and tender.
Pour the sauce mixture over the octopus and vegetables in the skillet. Stir well to evenly coat everything with the sauce.
Reduce the heat to medium-low and let the Nakji-bokkeum simmer for another 2-3 minutes to allow the flavors to meld together.
Once the dish is ready, you can garnish it with sesame seeds and thinly sliced green onions if desired.
Serve the Nakji-bokkeum hot with steamed rice or noodles.