In a large bowl, whisk together the soy sauce, lime juice, oil, garlic, and cumin. Add the mushrooms and shake them around, making sure to get the marinade on the inside of the caps. Let them marinate for 15-20 minutes.
Heat one side of your grill to medium-high for at least 10 minutes. Add the mushrooms (stem-side-down) and grill, covered, for 3-5 minutes. Flip and spoon some extra marinade on the inside of the caps, then cover and grill for 3-5 more minutes or until you have nice grill marks. Move the mushrooms to the other side and let them cook, covered, for 5 more minutes (the indirect heat will keep cooking them without burning them).
Meanwhile, in a medium bowl mix together the salsa ingredients. In a separate bowl, mix together the slaw ingredients.
Warm up your tortillas and add the mashed avocado down the center. Top that with the mushroom slices and the slaw. Top with salsa and pickle red onions, if using.