Bring a pot of water to boil. Add chicken and simmer for 10-12 minutes until fully cooked (Set the water aside to use it later for the sauce). Remove, let cool, and shred the meat and discard the skin and bones.
In the same pot, boil shrimp with clean water for 2-3 minutes until pink and opaque. Slice each shrimp in half lengthwise.
Follow package instructions to cook the noodles. Drain and rinse with cold water to prevent sticking. Wash and dry the lettuce, herbs, cucumber, and carrot. Slice cucumber and carrot into thin matchsticks.
Fill a large bowl with warm water. Dip one rice paper wrapper into the water for about 5 seconds to soften, then lay it flat on a clean, damp surface. Place a piece of lettuce on the lower third of the wrapper. Add vermicelli noodles on top, followed by a few slices of chicken, 2 shrimp halves (cut side up), cucumber, carrot, mint, and cilantro. Add basil and a piece of chive if desired.
Fold the sides of the rice paper over the filling, then roll tightly from the bottom up, ensuring a secure wrap. Repeat with the second roll.
Heat oil in a small saucepan over medium heat. Add minced garlic and sauté until fragrant (about 20 seconds). Add hoisin sauce, peanut butter, and water or chicken stock. Whisk until smooth and simmer for 1 minute. If needed, adjust thickness with more water. Pour into a small bowl and garnish with crushed peanuts and a drizzle of Sriracha if desired.
