Season the turkey: Toss shredded turkey with soy sauce, sesame oil, and lime juice. Set aside.
Prepare the wrappers: Fill a shallow dish with warm water. Dip one rice paper wrapper for 5–8 seconds until pliable but not floppy. Lay on a clean surface or a clean dish towel.
Add fillings: Layer vermicelli noodles, turkey, carrots, cucumber, cabbage, mango, mint, and green onions across the lower third of the wrapper.
Seal the rolls: Fold bottom edge over filling, fold sides inward, then roll tightly upward. Repeat with remaining wrappers.
How to make the peanut sauce
Whisk peanut butter, soy sauce, lime juice, maple syrup, sriracha, ginger, and garlic. Add warm water gradually until smooth and pourable. Add more sriracha to taste.