Whisk the lime juice, vegetable oil, curry paste, fish sauce and garlic in a large bowl. Add the shrimp; toss to coat. Refrigerate at least 30 minutes or up to 1 hour. Meanwhile, soak ten 8-inch bamboo skewers in water at least 30 minutes; drain. Thread the shrimp onto the skewers, rubbing any excess marinade on the shrimp; set aside.
Preheat a grill to medium high. Puree the coconut milk, 2 cups basil, the jalapeno and a pinch of salt in a blender, about 30 seconds. (Do not over-blend or the coconut milk might separate.) Set aside.
Melt the butter in a medium saucepan over medium-high heat. Add the scallion whites and cook, stirring occasionally, until softened, about 2 minutes. Add the rice, 1/2 cup water, the coconut milk-basil puree and 1/2 teaspoon salt. Bring to a simmer, stirring and scraping the bottom of the pot with a wooden spoon to prevent the rice from sticking. Reduce the heat to low. Cover and cook until the rice is tender and the liquid is absorbed, 15 to 17 minutes. Remove from the heat and keep covered.
Meanwhile, brush the grill grates with vegetable oil. Grill the shrimp skewers until well marked and just cooked through, 2 to 3 minutes per side. Fluff the rice with a fork, stir in the scallion greens and season with salt. Combine the bean sprouts, peanuts and remaining 2 cups basil. Top the lettuce leaves with the bean sprout mixture and shrimp skewers. Serve with the rice and lime wedges.