Mix the peanut sauce ingredients together, using enough water as needed to create a thick, creamy, but pourable dipping sauce.
Fill a large bowl with very warm water.
Fully submerge a single sheet of rice paper in the water. Shake off excess moisture, and place the sheet on a clean, flat work surface.
Place three cooked shrimp, side by side, on the top portion of the bottom third of the rice paper.
Turning a lettuce leaf to form a cup, add 1/8 of the carrots, 1/8 of the cucumber, 2 cilantro springs, and 3 mint leaves. Roll the leaf to create an enclosed packet.
Place the lettuce and veggie packet over the shrimp.
Pull the bottom of the moistened rice paper snugly over the shrimp and veggie packet. Then fold the left and right sides of the rice paper towards the middle to over the open ends of the shrimp and veggies.
Firmly roll the bundle towards the top of the rice paper until you have a neatly wrapped tube.
Wrap the spring roll in plastic wrap to prevent the rice paper from drying and become leathery.
Repeat with remaining ingredients to make a total of 8 spring rolls.
Refrigerate until ready to serve.
Serve with the peanut dipping sauce.