Shred mushrooms by running a fork from the top of mushroom stem to the bottom. Then pull the stem into separate pieces that resemble shreds. Roughly chop the mushroom caps. Place all pieces of the mushrooms into a bowl and set aside.
Put broth and onions into a pan. Stir occasionally and continue to cook for 2 minutes. Add more broth as needed. Add shredded mushrooms to the pan, stirring occasionally and continue to cook for another 2 minutes until mushrooms are moist. Add all of the remaining ingredients except for the bbq sauce. Stir to mix everything together. Cook for another 2 minutes. Add barbecue sauce, gently stir, and divide the mixture into 4 equal portions. Spoon onto burger buns.
Mix together avacado, mayo, and lime juice. Set aside. Combine both angel hair slaw and rainbow slaw in a large bowl. Add the agave, vinegar, salt, pepper, and avacado mixture. Stir to mix well. Divide into 4 portions. Spoon onto plates with the sandwiches. Serve and enjoy!
YIELD: 4 servings.