In a large bowl, whisk together miso, honey and soy sauce until smooth. Transfer ¼ cup to a small bowl, and whisk in mayonnaise; cover and refrigerate. Add green onions, garlic and ginger to remaining miso mixture.
Pat turkey dry. Add turkey tenderloin to green onion mixture; cover and refrigerate for 2 hours.
Remove turkey from bowl, discarding excess marinade. Pat turkey dry. Lightly spray turkey with nonstick cooking spray.
Heat a cast-iron grill pan over medium heat. Place turkey on pan, and lightly cover with foil. Cook, turning occasionally, until golden and nice grill marks have formed, and instant-read thermometer inserted into thickest portion registers 165°F, about 20 minutes. Let stand for at least 5 minutes before slicing. Serve on buns with miso mayonnaise and lettuce.
Prep Tips: If grilling on an outdoor grill, stick to indirect heat. The honey in the marinade makes it prone to burning! Looking to change it up? Try serving this tenderloin over jasmine rice.
