In a medium bowl, whisk together the soy sauce, sesame oil, garlic powder, ginger, and five spice powder. Add the pork and toss to coat. Let sit at room temperature for 20 minutes.
In a small bowl, beat the 2 eggs with 1/2 teaspoon salt.
Heat a large, non-stick skillet over medium-high heat with 1 tablespoon of the coconut oil until the oil is shimmering. Add the pork and cook until just cooked through, 3 to 4 minutes. Remove and reserve the pork.
Add the beaten egg to the hot skillet, tilt the pan to evenly distribute, then use a spatula to lift and move the egg around so it evenly cooks through and sets like a thin omelet, 2 to 3 minutes. Transfer to a cutting board to rest.
Return the skillet to the stovetop. Increase the heat to medium-high and add the remaining 1 tablespoon coconut oil. Add the mushrooms and cook, tossing occasionally, until they’re crispy golden brown in spots and tender, 4 to 5 minutes. Add the white/light parts of the green onions and 2 cups of the cabbage/slaw mix and cook for 2 minutes more.
Slice the egg into 1/2-inch thick by 2-inch long strips. Transfer the egg to the skillet, then add the pork and its sauce and toss to combine and heat through, 2 to 3 minutes.
Transfer the moo shu pork to a serving bowl and serve with sides of the dark green onion pieces, the remaining 1 cup cabbage mix, and lettuce cups.