Pat shrimp dry and sprinkle with salt and pepper. Heat oil over medium heat and add shrimp. Cook until shrimp turns pink and opaque throughout.
Mince garlic and grate ginger. Place all ingredients in a bowl and whisk until well blended. Fill lettuce cups with cooked shrimp, cucumber slices, avocado slices, carrot sticks, and cilantro. Roll up and enjoy the peanut sauce for dipping.