Put a medium-large pot on high fire, add a pinch of salt and bring to a boil. Add the shrimps and simmer for about 1 ½ minutes until the shrimps get a nice pink colour. Take out of the pot with a slotted spoon and add in a bowl filled with water and ice cubes for 5 minutes. Drain and cut each one lengthwise, cover with plastic wrap and refrigerate.
In the same water that the shrimps have been cooked bring the water to a boil, turn the heat off and cook the noodles for about 5 minutes and with time guidance from the package instructions. Immediately strain the noodles, add them to a bowl and pour the sesame oil. Keep aside.
In a deep bowl add the sugar, lime juice, rice vinegar, the fish sauce, and whisk. Add the julienned veggies and toss. Keep aside.
Assemble all the ingredients on your kitchen table. Start by pre-wrapping the lettuce. Open each leaf one by one and add some cilantro and 3 basil leaves, some of the julienned veggies and few noodles. Be careful not to overfill as it will be a problem to do the wrapping of the rice wrap. Wrap the lettuces and keep aside.
Have a large flat dish filled with room temperature water and dip with both hands, one at a time, the rice wrap moving it around to get soft, about 15 seconds. Lay on your cutting board and pat dry.
On the top part of the wrap place 3 mint leaves and on top of them 4 halved shrimps. Then leave some space and parallel to the shrimps add the pre-wrapped lettuce. Tag in the sides and fold over the bottom of the wrap over the filling and roll to a tight bundle. Place on a plate, the closing of the wrap facing down and cover with a damp cloth. Cover tightly with plastic wrap and refrigerate for 2-3 hours before serving.
30 minutes before serving take out of the refrigerator, cut in half in a slight angle and serve with the two sauces.