Heat a sauté pan over medium-high heat. Place ground beef in pan and cook; season with salt and pepper. Sauté for 3 to 5 minutes until golden brown. Chop mushrooms to approximately the size and texture of ground beef and sauté in a separate pan with 2 tablespoons olive oil for 3 to 5 minutes. Combine mushrooms and meat and set aside.
Heat sauté pan used for ground beef over medium-high heat. Add onions and sauté until golden brown. Add garlic and cook until fragrant. Add the mushroom/beef mixture and ground chili pepper. Sauté 2 to 3 minutes, stirring. Adjust seasoning with salt, pepper and lime juice.
To serve, toss shredded cabbage with salt, pepper, lime juice and cilantro. Please 2 tablespoons of shredded cabbage on a tortilla, and top with 2 tablespoons of mushroom and beef mixture. Top with a generous tablespoon of avocado salsa, and sprinkle with Cotija cheese to taste.
To make Avocado Salsa Verde: Combine all salsa ingredients and refrigerate for at least an hour.