Place the dried shiitake mushrooms and dried wood ear mushrooms in two medium bowls and cover with water for at least 30 minutes or until softened.
When the mushrooms are softened, squeeze out the extra liquid and cut off the stems from the shiitakes. Thinly slice the mushrooms. Set them aside with the rest of the sliced vegetables.
In a large bowl, toss the sliced chicken with ¾ teaspoon Umami Stir-Fry Powder or Diamond Crystal kosher salt and 1 teaspoon avocado oil. Set aside. Whisk together the eggs and fish sauce in a medium bowl. Heat a large non-stick or well-seasoned cast iron skillet over medium heat. Swirl in 2 teaspoons avocado oil when the pan is hot and pour in the eggs. Stir and scrape the pan constantly until you have soft, moist curds of scrambled eggs. Transfer the eggs to a platter.
Increase heat to medium high and add 1 tablespoon of avocado oil to the empty pan. Add the seasoned chicken and cook, stirring frequently until it is no longer pink. Transfer the cooked chicken to a plate.
Discard any liquid in the pan and add another tablespoon of avocado oil before tossing in the chopped mushrooms, cabbage, and carrot.
Sprinkle ½ teaspoon of Umami Stir-Fry Powder or Diamond Crystal kosher salt on the vegetables and stir-fry until the vegetables are tender crisp, about 2 to 3 minutes.
While the vegetables are cooking, whisk the All-Purpose Stir-Fry Sauce, arrowroot powder, and sesame oil in a small measuring cup or bowl.
When the vegetables are ready, stir in the reserved cooked chicken and pour the sauce over everything. Cook, stirring frequently, until the sauce is slightly thickened.
Turn off the heat and stir in the scrambled eggs and sliced scallions. Taste and adjust for seasoning if needed.
If you’re serving the Paleo Moo Shu Chicken in grain-free tortillas, heat them up in a dry skillet over medium heat until warm and softened.
Slather some Paleo Hoisin Sauce on a warm tortilla or lettuce wrap and build your own Chinese tacos or mini burritos with the Paleo Moo Shu filling.