Toss pork strips with 1 tbsp of the soy sauce. Heat oil in a lidded 12-inch skillet over medium-high heat. Add pork and cook 3 to 4 minutes, until no longer pink. Remove to a bowl with a slotted spoon.
Add cabbage, carrots and half the scallions to skillet. Cover and cook 3 minutes. Uncover and cook 5 minutes.
Add pork back to skillet along with remaining 1 tbsp soy sauce and 1/3 cup of the hoisin. Cook 2 minutes.
Meanwhile, wrap tortillas in damp paper towels and microwave 2 minutes. Spread each with 1/2 tsp hoisin. Spoon moo shu mixture onto wraps and sprinkle with some of the remaining sliced scallions.