Cook the rice vermicelli according to the package instructions then rinse with cold water until completely chilled. Using kitchen shears or a sharp knife, lift and slice the noodles a few times to cut them into more manageable pieces.
Mix together the sauce ingredients. Add 1 tablespoon of the sauce and 1 teaspoon cornstarch to the shrimp, let marinate for 15 minutes.
Combine the rice noodles, carrots, and green onions. Add all but 2 tablespoons of the sauce and toss to coat.
Heat a pan over high heat with a tablespoon of olive oil. Once the oil is shimmering add the marinated shrimp to the pan. Brown both sides, 2 to 3 minutes in total, or until cooked all the way through and the shrimps are fully curled. Transfer to a plate and let cook for 10 minutes.
Arrange some lettuce at the bottom of your bowl, then add some of the noodles. Continue layering the lettuce and noodles until all are used. Arrange the shrimp and cucumber over the salad. Drizzle with the remaining sauce and garnish with the peanuts.
Toss right before serving.