in a small bowl, whisk together the Hoisin Sauce, low-sodium soy sauce, rice vinegar, garlic, ginger, cornstarch, sesame oil, black pepper, and mirin. Remove 1/2 cup of the marinade and set it aside.
Add the cut chicken to the remaining marinade and stir to combine. Let it set for 10-15 minutes.
Heat another tablespoon of vegetable oil in the skillet over medium-high heat. Using tongs, remove the chicken from the marinade, letting the excess drip off. Add the chicken to the hot skillet, cooking until browned and cooked through or about 2-3 minutes. Work in batches, then remove to a plate and cover to keep warm.
Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat. Add the mushrooms and cook until browned. Remove to the plate with the cooked chicken.
If needed, add more vegetable oil to the skillet. Add the beaten eggs over medium-low heat. Cook until the eggs are set enough to flip. Using a spatula, flip and cook until set. Remove the eggs, cut them into thin strips, and cover to keep warm.
If needed, add a little more vegetable oil to the skillet. Add the cabbage and cook until slightly wilted. Add the chicken, mushrooms, and eggs back to the skillet. Whisk the sauce mixture that was set aside. Drizzle with the sauce, stir to combine, and toss to coat cooking over medium-low heat for several minutes until thickened.
Sprinkle with the scallions. For best results, serve promptly.