In a bowl, mix 2 tbsp. fish sauce, the brown sugar, garlic and 2 tbsp. water, stirring until the sugar dissolves. Put the pork in a resealable bag, pour in the fish sauce mixture and massage to coat the pork. Let the pork marinate at room temperature for at least 1 hour, or refrigerate overnight.
Bring a large pot of water to a boil. Meanwhile, in a small jar or plastic container with a lid, shake the lime juice, remaining 1/4 cup fish sauce, the granulated sugar and chile, if using, to make the dressing.
Add the vermicelli to the boiling water and cook until tender, about 5 minutes. Rinse under cold water; drain well.
In a large, heavy skillet, heat the oil over high heat until smoking. Add the pork, reserving the marinade. Cook, turning once, until the meat is golden-brown, 2 to 3 minutes. Pour the marinade into the skillet and cook, turning the pork once, until the marinade is thickened to a glaze, about 30 seconds. Transfer the pork to a cutting board; let rest for 5 minutes. Thinly slice against the grain.
Divide the noodles among bowls. Arrange the pork, cucumbers, carrots, lettuce, cilantro and mint on top. Pour on the dressing before eating.