Shred the lion's mane mushrooms. Remove and discard the cap on the king trumpet mushrooms and discard. Shred the stems.
Dice the onion and garlic. Add the oil to a pan and sauté the onion and garlic for 10 minutes on medium heat.
Add the shredded mushrooms and cook for 15 minutes on medium heat, stirring frequently.
Preheat the oven to 400 F.
For the sauce, combine the tomato sauce, apple cider vinegar, white vinegar, Worcestershire sauce, soy sauce, smoked paprika, garlic granules, and onion powder in a medium bowl.
Add ½ cup of the sauce to the mushrooms and onion mixture. Simmer the mushrooms and sauce mixture for 5 minutes over low heat. Transfer the mushrooms to a baking sheet.
Bake mushrooms for 35 minutes at 400 F, stirring halfway.
Add the remaining barbecue sauce, stir, and bake for 15 additional minutes.
When it's done, add the pulled mushrooms to buns and top with lettuce, red onion, slaw, or any other desired toppings.