In a large skillet, heat the vegetable oil over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain excess fat if necessary.
Stir in the minced garlic and ginger, cooking for an additional 1-2 minutes until fragrant.
Add the soy sauce, brown sugar, sesame oil, red pepper flakes, and black pepper to the skillet. Stir well to combine and simmer for about 5 minutes, allowing the flavors to meld.
In a separate large pan, add the sliced Napa cabbage and julienned carrot. Cook over medium heat, stirring occasionally, until the cabbage is wilted but still slightly crunchy, about 3-4 minutes.
To serve, place a generous portion of the wilted Napa slaw on a plate and top with the Korean ground beef mixture. Garnish with chopped green onions and sesame seeds.