Heat an outdoor grill or a grill pan over medium-high.
In a blender, working in batches if necessary, puree all the ingredients, except for the salt, pepper and shrimp. (You may need to thin it with water.) Season with salt and pepper.
Season the shrimp and grill until opaque in the center and charred in spots, 2 minutes per side. Serve alongside the gazpacho. Garnish the soup with extra chopped herbs and veggies.