Step 1
Blend chiles, garlic, sugar, fish sauce, 3 Tbsp. oil, and 1 tsp. salt in a blender until smooth.
Step 2
Transfer marinade to a medium bowl and add shrimp; toss to coat. Let sit 10 minutes.
Step 3
Heat remaining 1 Tbsp. oil in a large nonstick skillet over medium-high. Just when oil begins to smoke and working in batches if needed, add shrimp, leaving marinade behind, and cook, turning once, until lightly charred around the edges, about 1 minute per side.Remove pan from heat. Add basil and toss vigorously until basil is wilted.
Step 4
Transfer shrimp mixture to a platter. Serve with lime wedges alongside.