In a large skillet or wok, heat 1 tablespoon of cooking oil over medium-high heat. Add the garlic and ginger, sautéing for about 30 seconds until fragrant.

Add the sliced shiitake mushrooms and cook for 3-4 minutes until softened.

Stir in the napa cabbage and carrots, cooking for another 2-3 minutes until the vegetables are tender.

Add the shredded chicken, soy sauce, hoisin sauce, and sesame oil to the skillet. Stir well to combine and heat through, about 2-3 minutes. Season with salt and pepper to taste.

While the filling is cooking, warm the tortillas or moo shu pancakes in a separate pan or microwave until pliable.

To serve, place a generous spoonful of the chicken mixture onto a tortilla or pancake, sprinkle with chopped green onions, and roll it up or fold it over.