This dish was inspired by my trip to Hanoi and sitting on a short plastic stool on a busy sidewalk, having the most delicious grilled pork and imperial rolls over silky rice noodles. The crunch of the imperial roll with the deeply caramelized and salty pork, bright notes of lime, spice and cool cucumber round out this classic version.
Place the unground portion of the pork shoulder in the freezer for 30 minutes so it is easier to cut thinly.
In a large pot of boiling water, cook the vermicelli for 8 minutes, then rinse thoroughly in cold water. Take a handful of the noodles and set aside. Drain and place into 6 piles on a tray to dry out a little.
Cut the reserved handful rice noodles with scissor tips into 1-inch lengths and place in a mixing bowl. Add the ground pork, shrimp, half the shallots, minced garlic, minced carrot, 1/4 cup chopped cilantro, 3 tablespoons fish sauce, 2 tablespoons sugar and freshly ground pepper and mix all together very well.
Dip a rice paper into very hot water briefly and place on a cutting board to soften for 1 minute. Place 3 ounces of the shrimp and meat mixture into the middle of the rice paper to form a sausage shape 1 inch in diameter, then fold the ends in and roll into a tight roll. Set aside for later on a plastic wrap-lined sheet pan, making sure the rolls are not touching, or they will stick together. Continue with the remaining rice paper and filling to make 6 to 10 rolls. (These can be made in advance and frozen, then cooked from frozen.)
Remove the pork shoulder from the freezer and cut as thinly as possible into 1/8-inch-thick pieces. Place on a quarter-sheet tray or large platter. Top with 3 tablespoons fish sauce and 3 tablespoons sugar and let marinate for 30 minutes.
Combine the remaining 5 tablespoons fish sauce with 1 1/4 cups water, the lime juice, remaining 2 tablespoons sugar, the Thai chiles, the remaining whole garlic clove and remaining diced shallots, then mix well and set aside until ready to serve.
In 6 large individual bowls, arrange in equal portions the cold rice noodles, julienned cucumber, remaining carrot, scallion, mint, remaining cilantro leaves and romaine. Set aside the bowls until the rolls are fried and pork is grilled.
To assemble: Place the vegetable oil in a heavy-bottomed Dutch oven and heat to 350 degrees F.
Fry the imperial rolls two to three at a time, making sure they don't touch, until golden brown, 3 to 4 minutes. (If frying from frozen, they will take a little longer.)
Place on a paper towel-lined tray to drain. Cut each roll into 4 pieces.
Heat a grill to 400 degrees F or a broiler to high. Cook the pork until well caramelized on each side, about 4 minutes per side. Cut into 1-inch pieces.
Place equal portions of the grilled pork and an imperial roll on each noodle bowl. Remove the garlic clove from the sauce and pour about 2 ounces sauce into each bowl. Place the remaining sauce on the table and have the sriracha sauce available as well. Guests should mix the noodles and vegetables together with the sauce and add additional sauce as needed. Sprinkle on the fried shallots.