Chicken, shrimp, rice noodles, bean sprouts, mint leaves, and crisp lettuce are rolled up inside a rice-paper pancake for a light, refreshing appetizer.
Add rice vermicelli and teaspoon salt to boiling water; cook until al dente, about 3 minutes. Drain, rinse, and set aside.
Add chicken and remaining 1 teaspoon salt to boiling water. Reduce heat to medium-high; simmer chicken until cooked through, about 10 minutes. Remove chicken from water; reserve water. Slice chicken across the grain 1/8 inch thick and set aside.
Return water to a boil. Add shrimp; reduce heat to medium-high. Cook shrimp until opaque, 2 to 3 minutes. Drain. When cool enough, remove shells. Cut each shrimp in half lengthwise, devein, and set aside.
Fill a pan large enough to hold the rice paper with hot water. Dampen a clean kitchen towel with water; spread it out on a clean surface. Immerse 1 sheet of rice paper in the hot water until softened and flexible, about 1 minute. Transfer to dampened towel and smooth out. Fold paper in by 2 inches on right and left sides. Place 4 shrimp halves in a row, cut side up, 2 inches from bottom edge, and top with 2 to 3 slices chicken. Place 1 heaping tablespoon vermicelli on top and sprinkle with about 1 tablespoon bean sprouts. Cover with 5 to 6 mint leaves. Place 1 or 2 pieces of lettuce, curly sides out, on top. Fold bottom edge of rice paper over filling; roll up tightly to form a cylinder about 1 1/2 inches in diameter. Repeat until all the ingredients are used up.
Cut rolls into two or four pieces, and arrange on a serving platter. Top with peanuts and dabs of chile paste, and garnish with mint leaves. Serve with Peanut-Hoisin Sauce and Vietnamese Dipping Sauce.
Rolls can be made several hours in advance and stored at room temperature in an airtight container lined with dampened cheesecloth. Do not refrigerate or rice paper will toughen.