Slice the pork. Freeze the pork shoulder 30 minutes until firm but not frozen solid — this makes thin slicing much easier. Cut into 1/4-inch slices across the grain.
Marinate. Whisk all marinade ingredients in a large bowl. Add the pork, turn to coat every slice, cover, and refrigerate for at least 1 hour and up to overnight. Longer is better here.
Quick pickles. Dissolve the sugar and salt in the vinegar and water. Add the carrot and daikon, toss, and let sit at least 20 minutes while the pork marinates. Drain before serving.
Nuoc cham. Stir the sugar into the warm water until dissolved, then add the fish sauce, lime juice, garlic, and chile. Taste for balance — it should be sweet, salty, and bright all at once.
Cook the noodles. Boil the vermicelli according to the package (usually 4 minutes), rinse under cold water, and drain very well. Wet noodles dilute the dressing, so shake off as much water as possible.
Prep the cold components. Shred the lettuce, slice the cucumber, pick the herb leaves, and crush the peanuts. Keep everything chilled.
Grill the pork. Preheat a grill or grill pan to medium-high and oil the grates. Grill the pork in a single layer, 3 minutes per side, until charred at the edges and cooked through. Work in batches — crowding steams the meat instead of caramelizing it. Do not place cooked pork back on the plate or with utensils that touched raw pork.
Check doneness. Thin slices cook fast, but confirm the thickest piece reaches 145°F (63°C) internal temperature, then rest 3 minutes.
Assemble. In each bowl: a bed of noodles, then lettuce, cucumber, pickles, and herbs on one side; sliced pork on the other; peanuts over the top. Serve the nuoc cham on the side.