Cook brown rice (use rice cooker or pasta method: boil in large pot for 30 minutes and drain, put back into pot and close with lid for 10 minute). Set aside and cool to room temperature.
Season cooled rice by putting it into a large bowl. Season with rice wine vinegar, coconut sugar, and salt. Set aside.
Heat a large pan to high. After couple minutes, add oil, and lower heat to medium-high.
Sauté king mushrooms in an even layer, do not over fill pan. Cook each side about 3-4 minutes until juices cook out of mushrooms.
Set aside cooked mushroom on a plate, season lightly with a pinch of salt and pepper. Let cool.
Make creamy sauce by adding the Phyters, miso paste, lime juice, rice wine vinegar, tamari, coconut sugar, ginger, garlic, and sesame oil in a blender. Blend on high, slowly drizzle plant-based milk while blending to desired consistency. Set aside in small bowl.
Start plating the wrap by plating the lettuce leaves on a plate. Spoon the seasoned rice onto the lettuce, and lay mushrooms on top of rice. Lay cucumbers and green onions on top of the mushrooms. Add any optional ingredients to garnish.
Spoon sauce over the lettuce wrap.
Pick up lettuce and wrap into a tight ball/package and enjoy!