1. Combine sugar, water, vinegar, salt, garlic, and chile in a saucepan and bring to a boil.
2. Once boiling, reduce heat and simmer for 10 minutes.
3. After that time, remove the sauce from the heat and set it aside to cool.
4. Bring lightly salted water to boil in a large pot.
5. Once boiling, add the shrimp and let them cook for 2 to 3 minutes.
6. After that time, remove the shrimp from the pot of boiling water and set them aside to cool.
7. Bring another large pot of lightly salted water to boil.
8. Once boiling, remove it from heat, add the vermicelli noodles, let sit for 4 to 8 minutes, or cook based on package instructions.
9. After that time, drain and rinse the noodles in cold water, then set aside.
10. Gather the shrimp, mango, carrots, cucumber, lettuce, and rice paper around a damp cutting board.
11. Lightly dip a piece of rice paper in a bowl of warm water, lay the damp rice paper on the damp cutting board, place a piece of butter lettuce on it (close to the bottom), then the mango, carrots, and cucumber slices, then the noodles, and then 2½ ounces of shrimp.
12. Grab the lower part of the rice paper, roll it over the ingredients, fold in the sides eventually, and then roll the wrap closed.
13. Repeat steps 11 & 12 until 10 fresh rolls are made.
14. Store fresh rolls in individual plastic wraps to keep them freshest, in the fridge, for up to 5 days.
15. Serve the rolls with the dipping sauce, and enjoy!