Make gochujang sauce by whisking all ingredients in a small bowl until combined. Set aside.
For the bulgogi beef, combine all the marinade ingredients in a bowl. Add beef slices and stir until combined. Let it marinade while you prepare the other ingredients.
Shred carrot or chop with a knife into matchsticks. Heat up sesame oil in a large nonstick skillet over medium heat. Add shredded carrot, salt and a splash of water. Stir and cook for 1-2 minutes or until tender. Remove from heat and set aside.
Heat up 1/2 tsp oil in the same nonstick skillet over medium heat. Add eggs and cook them over-easy style. Remove from heat and set aside.
Heat up the same nonstick skillet over medium-heat heat. Add marinated beef (drain slightly and discard excess marinade) and stir-fry for 1 minute or until no longer pink. Remove from heat and set aside.
Assemble
Lay a tortilla flat on a plate or clean benchtop. Add salad greens, rice, carrot, beef, egg, sesame seeds and top with gochujang sauce. Fold the sides in and then roll upwards tightly. Cut in halves with a knife if desired.
Repeat with the second tortilla and remaining ingredients.