Make the dipping sauce. Combine all of the ingredients into a food processor and pulse until creamy. Reserve six tablespoons and save the rest in the refrigerator for future use (or freezer.)
Create an assembly line of the vegetables for the spring rolls (this just helps you keep organized).
Fill a shallow dish with warm water. One at a time, dip a rice wrapper sheet into the water for 5 to 10 seconds. Remove and place on a flat surface, like a cutting board or plate.
In the middle of one of the rice wrappers, lay 2 avocado slices (only do 1 if that’s all can fit) down, 1 pinch of cilantro and 1 pinch of mint, cucumber noodles, carrots, and top with lettuce. Squeeze over with 1/2 lime wedge and season with pepper.
Fold the bottom half of the rice paper wrapper over the filling. Holding firmly in place, fold the sides of the wrapper in. Then, pressing firmly down to hold in place, roll the entire wrapper horizontally up from the bottom to the top. Turn the roll so that the seam faces down and the avocado faces up.
Continue with the remaining ingredients and rice wrappers to make four. Place on a plate and cover with plastic wrap and refrigerate, if not serving immediately.
Serve the spring rolls with the dipping sauce.