Bring a pot of water to a boil and cook the shrimp for 2-3 minutes until pink and opaque, then immediately transfer to an ice bath to chill.
Once cooled, peel the shrimp and slice them in half lengthwise to create thin pieces.
Julienne the cucumber and carrots into thin matchsticks and slice the avocado into thin wedges.
Prepare the dipping sauce by whisking together the tamari, rice vinegar, grated fresh ginger, and minced garlic in a small bowl.
Fill a shallow dish with warm water and dip one rice paper wrapper for 5-10 seconds until it begins to soften, then lay it flat on a clean surface.
Place a few mint and cilantro leaves in the center of the wrapper, followed by 3-4 shrimp halves, cucumber, carrots, and a slice of avocado.
Fold the bottom of the wrapper over the filling, tuck in the sides, and roll tightly to seal.
Repeat the process with the remaining wrappers and ingredients, serving immediately with the ginger-tamari sauce.