Step 1

Place 8 ounces peeled and grated carrots and 8 ounces peeled and grated daikon in a fine-mesh strainer set in the sink or in a bowl. Sprinkle with 1 teaspoon kosher salt, and toss and massage the salt into the vegetables with your hands. Squeeze out as much excess liquid as you can. Discard the liquid and transfer the vegetables to a 24-ounce canning jar or medium heat-proof bowl.

Step 2

Heat 2/3 cup water, 1/3 cup granulated sugar, and 1/3 cup distilled white vinegar in a small saucepan over medium-high heat until sugar is dissolved, about 2 minutes.

Step 3

Pour over the vegetables and make sure they are fully submerged in the brine. Cover and let sit at room temperature for at least 1 hour before using.

Step 4

Stir 1 minced small shallot, 1/4 cup granulated sugar, 2 tablespoons minced garlic, 2 tablespoons fish sauce, 1 tablespoon neutral oil, 1 tablespoon soy sauce, and 2 teaspoons black pepper together in a large bowl or gallon zip-top bag. Add 1 1/2 pounds sliced boneless pork shoulder and toss to coat. Cover the bowl or seal the bag. Refrigerate for at least 1 hour or up to overnight.

Step 5

Arrange an oven rack in the upper third of the oven and heat the oven to 375ºF. Line a rimmed baking sheet with aluminum foil and fit a wire rack on top. Coat the rack with cooking spray. Arrange the marinated pork into a single layer on the rack (it’s okay if the rack is crowded).

Step 6

Roast until the pork is almost cooked through and registers 140ºF, about 10 minutes. Turn on the broiler and broil until the pork is charred in spots, 2 to 5 minutes per side. Let cool slightly while you toast the bread and assemble the sandwiches.

Step 7

Reduce the oven temperature to 375ºF. Split 4 Vietnamese baguettes in half with a serrated knife. Close the bread back up, then wrap in aluminum foil. Bake until the outside is lightly crispy to the touch, 5 to 7 minutes.

Step 8

Assemble each sandwich: Open up the bread again. Spread 1 tablespoon of the mayonnaise on the cut side of the bottom half. Spread 1 tablespoon of the pâté if desired on top of the mayonnaise. Top with about 4 jalapeño slices if desired, 1/4 cup of the pickles (drained), 1/4 of the pork slices, and a few dashes soy sauce. Top with 1 cucumber spear and 4 fresh cilantro sprigs. Close the sandwich with the top of the baguette and cut in half with the serrated knife if desired.