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Step 1
Combine salt and sugar in a small bowl and mix thoroughly.
Step 2
Place pork shoulder roast in a zip-top bag. Pour salt-sugar mixture into bag and massage mixture evenly into meat. Seal bag, trying to avoid leaving much air inside. Place bag in refrigerator for 24 hours. Roughly every 8 hours, massage bag and flip it over to ensure even distribution of the cure.
Step 3
Set up an immersion circulator and preheat a water bath to 145°F (63°C).
Step 4
Remove roast from zip-top bag and place on a cutting board. Discard liquid in bag and blot roast completely dry. Using kitchen twine, tie roast at 1/2-inch intervals to form a neat cylinder.
Step 5
Place roast back in zip-top bag and add soy sauce and mirin. Seal bag using the water-displacement method. Alternatively, if using a vacuum sealer, transfer the roast to a sealable vacuum bag, add soy sauce and mirin, and seal.
Step 6
Place bagged roast in water bath and cook for 20 hours.
Step 7
Remove bag and place in an ice bath to chill roast thoroughly. Remove roast from bag and blot dry.
Step 8
If Finishing Under the Broiler: Place roast on a rimmed baking sheet. Adjust oven rack so that the roast will be about 1 inch away from the broiler element. Preheat broiler to high. When broiler is hot, place roast under broiler, turning frequently, until exterior is charred, about 5 minutes.
Step 9
If Finishing With a Handheld Torch: Turn on torch and char exterior of roast on all sides.
Step 10
The roast can be sliced and served immediately, or sliced and stored for future use (see Make-Ahead and Storage, below).