Preheat the oven to 400°. Spread the pistachios in a pie plate and toast for about 5 minutes, or until the nuts are lightly browned. Let the pistachios cool completely, then coarsely chop them.
In a blender, combine the pistachios with the basil, mint, lime juice, vinegar, mustard, cayenne and olive oil. Blend at low speed until pureed. Add the ice cubes and blend at high speed until the sauce is very smooth. Scrape the basil emulsion into a small bowl and season with salt and black pepper.
Light a grill or heat a lightly oiled grill pan. Brush the shrimp with vegetable oil and season with salt and black pepper. Grill them over a hot fire for 1 minute per side, or until lightly charred and just cooked through. Alternatively, cook the shrimp in the grill pan over high heat for 1 to 2 minutes per side. Serve the hot shrimp with the basil emulsion alongside for dipping.
The basil emulsion can be refrigerated overnight. Whisk well before serving.