Combine shrimp, 2 tablespoons fish sauce, 2 tablespoons oil, and turmeric in a large bowl; toss to coat. Let stand for 30 minutes.
Purée 4 tablespoons fish sauce, 2 tablespoons oil, cilantro, and remaining ingredients in a blender or food processor until a coarse mixture forms; transfer dipping sauce to a small bowl and set aside.
Build a medium-hot fire in a charcoal grill, or heat a gas grill to high. Oil grill grates. Shake excess liquid from shrimp and place shrimp on grill. Cook, turning occasionally, until shrimp are charred and cooked through, 5-6 minutes.