Mix all sauce ingredients in a bowl until smooth and well combined, then set aside
Heat olive oil and sesame oil in a skillet over medium-high heat
Season shrimp with salt and pepper, then cook until pink and opaque
Add garlic and ginger paste, sauté briefly until fragrant
Remove shrimp from heat and allow them to cool slightly
Lay out lettuce leaves on a clean surface to form “boats”
Add sliced avocado evenly into each lettuce leaf
Place cooked shrimp on top of the avocado
Sprinkle carrots, green onions, and cilantro over the filling
Drizzle prepared sauce over each lettuce boat before serving