How to Make It
In a medium bowl, mix the vinegar with the granulated sugar and the salt until they dissolve. Add the carrots and let stand until just softened, about 30 minutes.
Meanwhile, in a small saucepan, combine the brown sugar with the fish sauce. Cook over moderate heat, stirring occasionally, until the sugar is dissolved and the sauce is thick, about 4 minutes. Pour the sauce into a small bowl.
In a very large skillet, heat the oil until almost smoking. Add half of the pork and cook over high heat until browned in spots, about 2 minutes per side. Using a slotted spoon, transfer the pork to a platter. Repeat with the remaining pork.
Add the chiles, garlic, shallots, lemongrass and ginger to the skillet and cook over moderate heat until fragrant, about 1 minute. Add the chicken stock and cook, scraping up any browned bits from the bottom of the pan, about 1 minute. Add the brown-sugar sauce and cook over moderate heat, stirring, until thickened, about 3 minutes.
Cut the pork into 2-inch strips. Return the pork and any accumulated juices to the skillet and cook until the meat is coated with sauce, about 30 seconds. Transfer to plates. Drain the carrots, sprinkle over the pork and serve at once with the rice noodles, bean sprouts, sliced cucumber, mint and chopped peanuts.