In a mixing bowl, whisk together the soy sauce, hoisin sauce, and cornstarch.
Heat the vegetable oil in a large skillet over medium-high heat. Add the shiitake mushrooms, Napa cabbage, carrots, sliced shiitake mushrooms, scallions, garlic, and ginger. Sauté for 5-7 minutes, until the vegetables are tender.
Pour the soy sauce mixture over the vegetables and stir to combine. Cook for an additional 2-3 minutes, until the sauce has thickened.
Warm the moo shu pancakes in the microwave for 10-15 seconds or according to package instructions.
To serve, spread a small amount of hoisin sauce on each moo shu pancake. Add a spoonful of the vegetable mixture to the center of the pancake, fold in the sides and roll up like a burrito.
Serve the moo shu vegetable hot, garnished with additional scallions or sesame seeds if desired. Enjoy!