Process the 2 cups pistachios in a food processor bowl until finely chopped but not a paste. Butterfly shrimp just enough so they sit upright.
Beat egg whites with ice water. Coat each shrimp with egg white mixture, then dip into ground pistachios. Place coated shrimp upright on a cookie sheet. Bake in a 350 degree F oven for 8 to 10 minutes.
Meanwhile, for dipping sauce, place garlic, green onion, cilantro, mint, and the 1/2 cup pistachios in a food processor bowl fitted with a metal blade; cover and process until a paste forms. Add coconut milk, lime juice, and chili paste; process until nuts are very finely chopped and mixture is well combined.
Serve the shrimp warm with room-temperature dipping sauce. Makes 20 to 24 servings.