In a large skillet, cook the ground beef over medium-high heat until no longer pink. Drain off excess grease.
To the skillet with the ground beef, add the sesame oil, rice vinegar, mushrooms, and onion. Cook, stirring, until the onion and mushrooms start to soften, about 3 minutes. Add the garlic, coleslaw mix, and carrots to the skillet. Cook, stirring, for about 5 more minutes, or until cabbage starts to wilt.
Add the green onions, salt, soy sauce, hoisin sauce, sugar, ginger, and pepper. Cook and stir until the vegetables are tender, about 2-3 more minutes. Taste and season with additional salt and pepper, if necessary.
Serve the mixture in tortillas or on top of rice with hoisin sauce and additional optional toppings.