Step 1

Pulse chiles, sugar, 2 teaspoons salt, and lime leaves in a small food processor until finely minced and sugar and salt are tinted green, about 20 pulses, stopping to scrape down sides and bottom of processor as needed. Add scallion greens, sweetened condensed milk, and lime juice. Process until creamy and green, about 30 seconds. Refrigerate sauce until ready to use.

Step 2

Melt butter in a small saucepan over medium-low. Remove from heat, and stir in basil, garlic, and 1/2 teaspoon salt. Pour half of butter mixture into a small bowl, and set aside; reserve remaining butter mixture in saucepan for brushing shrimp during grilling.

Step 3

Devein and rinse shrimp; pat dry with paper towels. Skewer each shrimp, from tail up to head, on an 8-inch skewer. Sprinkle shrimp evenly with remaining 1/4 teaspoon salt. Preheat a gas grill to high (450°F to 500°F). Place shrimp on grill grates; grill, uncovered, brushing with reserved melted butter mixture in saucepan and flipping shrimp often, until tail flesh is opaque and cooked through, 4 to 5 minutes. Remove skewers from grill, and let cool slightly, about 5 minutes. Remove shrimp from skewers, and pour remaining melted butter over shrimp. Serve with green chile sauce for dipping. —ANDREA NGUYEN