Prepare the ingredients by slicing the chicken and vegetables.
Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat.
Add sliced chicken to the skillet and stir-fry until no longer pink, about 5-7 minutes.
Add in the garlic, stirring for about 30 seconds until fragrant.
Introduce the napa cabbage, carrots, and shiitake mushrooms to the skillet.
Pour in soy sauce, hoisin sauce, and sesame oil, stirring to combine.
Stir until everything is well mixed and heated through, about 2-3 minutes.
Serve the Moo Shu Chicken mixture alongside warm pancakes or tortillas.
Garnish with sliced green onions before serving.