Prep the lettuce and veggies. Separate and wash the lettuce leaves.
Pat them dry so they stay crisp. Chop cucumber, shred carrot, and slice green onions. Set aside with herbs.
Mix the sauce. In a small bowl, whisk chili paste, soy sauce, fish sauce, honey, sesame oil, rice vinegar, and the zest and juice of half the lime.
Taste and adjust: add more chili for heat, honey for sweetness, or vinegar for tang.
Season the shrimp. Pat shrimp dry with paper towels. Toss with a pinch of salt, black pepper, and half the minced garlic.
Heat the pan. Set a large skillet over medium-high heat. Add the neutral oil and let it shimmer.
Cook the shrimp. Add shrimp in a single layer.
Sear 1–2 minutes per side until just pink and curled. Don’t overcook. Remove to a plate.
Build the flavor. Lower heat slightly.
Add remaining garlic to the pan for 15–20 seconds until fragrant, then pour in the sauce. Simmer 30–45 seconds to thicken slightly.
Coat the shrimp. Return shrimp to the pan and toss to coat in the glossy sauce, about 30 seconds. Squeeze in a bit more lime if needed.
Assemble the wraps. Fill lettuce leaves with shrimp, then top with cucumber, carrot, green onions, cilantro or mint, and a sprinkle of sesame seeds.
Serve with extra lime wedges.