In a bowl, toss the shrimp and lime juice; set aside. In a small food processor, puree the shallots, brown sugar, salt, lime leaves, nuts, garlic, chiles, and ginger. In a large skillet, heat the oil over medium-high heat. Once hot, add the spice mixture and cook, stirring frequently, until oil separates from the paste, 3–4 minutes. Stir in the coconut milk, remove from heat, and set aside to cool to room temperature, then pour the liquid over the shrimp, cover, and refrigerate at least 2 and up to 4 hours.

Build a hot charcoal fire in a grill. Thread the shrimp onto the skewers and grill, spooning more marinade over the shrimp as they cook and turning occasionally, until charred, 3–5 minutes. Serve hot.