Heat a pan over medium-high heat. Add the ground beef (or tofu) and spread it out in an even layer so it can brown. Let it cook undisturbed for about 1–2 minutes.
Add the bulgogi seasoning: soy sauce, sesame oil, garlic, ginger, and black pepper. Stir everything together and cook for another 2–3 minutes, until the meat is fully cooked and the sauce is absorbed and slightly caramelized. Remove from heat.
In a small bowl, mix the bibimbap sauce ingredients: gochujang, sesame oil, water, and sesame seeds. Mix until smooth and drizzle-able.
Dip each rice paper sheet in water for ~5 seconds until pliable. Lay them overlapping in a 2 × 2 square on a clean surface.
Layer the fillings in this order: Cabbage, Bulgogi, Carrot, Kimchi, Cucumber, then drizzle some of the sauce on top.
Fold the bottom edge up, fold in the sides, then roll forward tightly.
Optional: Heat oil in a pan over medium heat. Cook the wrap seam-side down until golden and crispy (~3 minutes per side). Let rest 1 minute, then slice.
