Prepare the shrimp: If using raw shrimp, boil or steam them until pink and cooked through (about 3-5 minutes). Halve each shrimp lengthwise after cooling.

Prepare the vermicelli: Cook the rice noodles according to package directions, usually by soaking in hot water until tender. Drain immediately and rinse with cold water to stop cooking and prevent sticking. Set aside.

Make the peanut sauce: In a small saucepan or microwave-safe bowl, combine peanut butter, Hoisin sauce, soy sauce, sesame oil, minced garlic, and sugar (if using). Heat gently while stirring until smooth. Whisk in the hot water, one tablespoon at a time, until the sauce reaches a thick but pourable consistency. Stir in lime juice and taste; adjust seasoning if necessary.

Prepare the wrappers: Fill a shallow dish wide enough to submerge a rice paper wrapper with warm water. Dip one rice paper wrapper into the water for about 10-15 seconds until pliable, but not overly soggy. Lay it flat on a clean, damp cutting board or piece of plastic wrap.

Assemble the rolls: Arrange a small amount of lettuce near the bottom edge of the wrapper. Top the lettuce with a small tangle of vermicelli noodles, a few strips of julienned carrot, mint leaves, and cilantro. Place two shrimp halves, pink side down, about 1 inch from the bottom edge.

Fold the rolls: Fold the bottom edge up over the filling. Fold in the sides tightly towards the center. Then, gently but firmly roll the wrapper upwards until you have a compact, tight cylinder. Repeat with remaining ingredients.

Serve immediately or cover lightly with a damp cloth to prevent drying out. Serve the Vietnamese noodle rolls alongside the warm peanut dipping sauce.