1. Pour 2 cups of the simmering water into a 6-quart heatproof container with a tightfitting lid, then remove remaining water from heat. Add salt and sugar to the heatproof container and stir until dissolved. Add garlic, chiles, peppercorns, and pork. Top with remaining 8 cups of now-tepid water to fully cover meat. Submerge meat if necessary by filling a resealable bag with water and placing it on top. Cover and refrigerate 12 hours or overnight.
2. When pork is ready, remove from liquid, rinse, pat dry with paper towels, and place fat side up in a roasting pan. Allow to come to room temperature for about 30 minutes. Meanwhile, heat the oven to 400°F and arrange a rack in the middle. Roast pork until internal temperature reaches 165°F, about 1 hour 45 minutes. Let cool to room temperature, at least 45 minutes, then slice thinly, about 1/8 inch thick.

1. Combine vinegar, sugar, and salt in a small saucepan over medium heat. Once sugar and salt have dissolved, remove from heat, add carrots, and stir to coat in pickling mixture. Let stand until carrots have softened, at least 30 minutes or overnight. Drain well and set aside.

1. Slice off top 1/3 of baguettes lengthwise and set aside. Remove enough of the bottom interiors so that the filling can fit easily.
2. Spread 1 tablespoon of the mayonnaise on each upper 1/3 of baguette and 2 tablespoons on each bottom. Crumble 1/2 of the pâté (if using) on each bottom section, then top with sliced pork (there may be some left over), cucumber, cilantro leaves, pickled carrots, and jalapeños. Sprinkle each sandwich with soy sauce and close with the upper parts of the baguettes. Place 10 toothpicks approximately 1 inch apart to secure the sandwiches and slice into about 10 (1-1/2-inch) pieces. Serve.

Beverage pairing: Tiger Beer, Singapore. Banh mi are wonderful street food and could be washed down by any number of beverages. But a light lager such as Tiger from Singapore—which is found all over Vietnam—is a good choice. Its thirst-quenching rush of bubbles will refresh the palate and salve the heat (if you put a lot of chile on the bun).