Prepare the dipping sauce: Add all ingredients except water to a small bowl. Gradually add water and whisk to blend. Set aside.
Prepare the rice paper wrappers: Pour warm water into a shallow bowl. Dip a rice paper wrapper into the warm water for about 15-20 seconds. The wrapper should be soft, but slightly firm and pliable. Remove from the water and place flat onto a cutting board; plastic works well.
Fill the rolls: Place 4 slices of shrimp, a few sticks of carrot, cucumber, red pepper, and cabbage on the bottom 1/3 of the rice paper. Add a small amount of noodles, a slice or 2 of avocado, 2 or 3 mint leaves, and 1/2 teaspoon of sesame seeds. Place 1/2 of a lettuce leaf on top. Do not overstuff the roll.
Fold the bottom half of the wrapper over the filling, pressing down to create a seal, then fold the sides of the wrapper towards the center, tucking in the filling. Roll the wrapper up, like a burrito. Repeat with the remaining wrappers and filling.
Slice each roll in half diagonally and serve with dipping sauce.
To store: Wrap rolls individually in plastic wrap.