Prepare the pork shoulder for roasting. Preheat your oven to 350F/177C. Measure out all of the ingredients for the broth: water, soy sauce, brown sugar, sesame seed oil and mirin. Combine everything in a medium-sized Dutch-oven or oven-safe pan. Add the chopped ginger and crushed garlic. Bring the mixture to a simmer over medium heat. Remove the pork shoulder from packaging and place directly into prepared broth. The meat should be covered only half way.

Bring the mixture back up to a simmer. Cover the Dutch-oven with a lid. If using an oven-safe pan, make sure the lid fits tightly. Place into preheated oven and roast for 3 ½ to 4 hours, turning the meat half way through. If too much liquid evaporates, add a small amount of water to replenish. Alternatively, the pork shoulder can be prepared in a slow-cooker. Follow all instructions as above and cook the pork shoulder for 6 hours on 'high' setting.

After 3 ½ to 4 hours, pork shoulder will be very tender and fall apart. Remove the meat from the oven and cooking pan and set into a large bowl. Use two large forks or tongs, pull the meat into small pieces.

Strain the cooking broth through a fine-mesh strainer. Skim off any impurities and fat from the top. Discard pieces of ginger, garlic and impurities. Pour the broth into a sauce pan and bring to a simmer of medium heat. Simmer for a few minutes to thicken the sauce. Reserve ¼ cup of the sauce for later. Pour prepared sauce over the pulled pork and toss to coat all of the meat.

For the red cabbage slaw, thinly slice the cabbage into shreds and place into a large bowl, along with grated carrots, sour cream and lime juice. Season to taste with salt and toss the ingredients together until well coated in the sour cream.

To assemble the sandwiches, first spread mayonnaise and pepper sauce onto the bread. Toast the bread in a pan, on a griddle or under the oven broiler until golden. Add a generous amount of pork meat onto each sandwich and top with the cabbage slaw. Add additional sauce on the top, if desired. Enjoy warm.