For the cashew sauce: Whisk the coconut milk, cashew butter, agave nectar, lime juice, fish sauce and chili garlic sauce in a bowl with 1 tablespoon water until smooth.
For the summer rolls: Bring 4 cups water to a boil in a small pot and add the shrimp. Cook until the shrimp turn pink, about 2 minutes. Drain well and let the shrimp cool. Slice the shrimp in half lengthwise.
Prepare the vermicelli according to package instructions and splash with mirin. Hold the noodles in the colander to allow the mirin to drain and the vermicelli to cool.
Meanwhile, halve, pit, peel and slice the avocado into 1/4-inch slices. Peel, pit and slice the mango into thin strips and set aside.
Fill a large bowl with warm water. Place a spring roll wrapper in the water and soak until soft, about 2 minutes. Gently transfer the wrapper to a dry board and blot excess water with a paper towel. The paper can rip easily if it soaks too long, so be sure to remove it from the soaking water as soon as it's pliable.
Allowing the summer roll ingredients to chill before rolling produces best results. Starting an inch from the bottom of the wrapper, place 3 Thai basil leaves face down in a row. Next, place 3 shrimp face down in a row on the basil. Place 2 slices of avocado across the shrimp, top with some vermicelli and finish with 2 mango slices. Fold in the sides of the wrapper and roll tightly. Place the roll on a tray with the Thai basil-side up and cover with a damp towel. Repeat with the remaining ingredients. Serve the rolls with the cashew dipping sauce on the side.
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