Heat a drizzle of sesame oil in a pan over medium heat. Add the tofu torn into chunks and cook until golden on all sides. Once cooked, add a splash of soy sauce for flavor and stir for another minute before removing it from the pan.
Using the same pan, add the mushrooms. Cook them for a few minutes until they release their moisture and reduce in size. Add the cooked tofu back to the pan and toss in freshly chopped parsley. Mix well to combine.
Soak the the rice papers in warm water for 30 seconds/1 minute (a few at a time) until they become soft and pliable. Lay each rice paper on a clean surface, ensuring they don’t overlap to avoid sticking together. Pat them gently with a kitchen towel to remove excess water.
Place a rice paper sheet on a clean, dry surface. Add a portion of the tofu-mushroom filling near one edge. Fold the sides inward, then roll it tightly to form a neat roll. Repeat with the remaining rice papers and filling. Oil them slightly so they don't stick together.
Place the assembled rolls in a steamer and steam them for 5 minutes. This step softens the rolls further and melds the flavors together.
While the rolls are steaming, prepare the dipping sauces. Mix peanut butter with tahini and add a splash of water to thin it to your desired consistency. In a separate bowl, mix soy sauce with a splash of water to dilute it
Transfer the steamed rolls to a serving plate. Drizzle with the peanut-tahini sauce, soy sauce, and a few drops of chili oil. Serve immediately and enjoy!