Soften Rice Paper: Fill a large shallow plate with warm water. Dip one rice paper wrapper into the water for about 10 seconds, or until softened but still slightly firm. Transfer it to a clean work surface.
Arrange Shrimp: Place one cooked shrimp near the bottom third of the wrapper, cut-side down if halved, to create a neat presentation.
Add Mint: Layer a few fresh mint leaves over the shrimp.
Add Vegetables: Top with a small handful of shredded cucumber followed by shredded cabbage.
Add Peanuts: Sprinkle a small amount of chopped peanuts over the vegetables.
Add Noodles: Place a small bundle of cooked rice noodles on top of the filling, keeping everything centered.
Roll the Summer Roll: Fold the bottom edge of the wrapper over the filling, fold in both sides, and roll tightly into a compact cylinder. Repeat with the remaining wrappers and filling ingredients.
Mix Sauce Base: In a small bowl, combine the sugar and chopped green onion.
Add Liquid Ingredients: Stir in the mirin, lime juice, soy sauce, sesame oil, and fish sauce until the sugar dissolves and the sauce is well combined.
Serve: Arrange the shrimp summer rolls on a serving platter and serve immediately with the sesame-soy dipping sauce.