Bring a pot of water to a boil over high heat and add vermicelli noodles. Cook for 2 minutes until soft. Transfer the noodles to a bowl with a strainer to completely drain out any water.

Fill a large shallow bowl with warm water, about 1 to 2 inches high. Take one rice wrapper at a time and quickly dip it into the warm water for one second, or according to package directions. Shake off excess water. The wrapper will start to soften and feel a bit sticky. Transfer the wrapper onto a clean dry flat surface.

Place some cucumbers and carrots in the center of the rice wrapper into a log shape, leaving 2 inches of space on each side. Top with about 2 tablespoons of vermicelli noodles, a few basil leaves, and 2-3 tablespoons of chicken.

Roll the wrapper up tightly from the bottom but gently so that you don't tear it. Roll it up halfway over top of the noodles. Then fold over the left and right sides inward. Then continue to tightly roll the wrapper to seal the mixture inside. If the wrapper doesn't feel soft and pliable, apply some water to your fingers and to the wrapper to help it soften.

Make the peanut sauce: Combine hoisin sauce, peanut butter, water, lime juice, and honey. Stir well with a spoon until smooth and uniform. Sprinkle some chopped roasted peanuts on top.