Preheat oven to 350f
Place pork shoulder on baking sheet or cutting board and sprinkle on dry rub. Massage into meat and make sure all parts of the pork is covered.
Place a lightly oiled dutch oven over medium high heat. Once temperature has been reached, lay in pork and sear on all sides. You are looking for a nice crush here so don't be shy. About 4 minutes per side.
Once all sides of the meat is seared, add in the braising liquid ingredients and place it back on stove top over high heat. Once a simmer has been reached, place on the cover and place in the preheated oven for 90 minutes.
After 90 minutes, remove the dutch oven from the oven, remove lid, and flip the pork shoulder over. Be careful not to splash yourself with hot braising liquid. Cover the pork and place back in the oven for an additional 90 minutes.
Let's kick on with the slaw. Nothing fancy here. Add the cabbage, leek, cilantro, salt, mayo, and lemon juice in a bowl. Stir and then let chill in the fridge until ready to serve.
After the pork is done cooking, remove from oven and let rest on stove top with lid on for 10 minutes. After the 10 minutes, shred the pork with two forks. I like to shred directly in the braising liquid but maybe give it a taste test to make sure it's not too spicy for you.
Now build the sandwich. I like to toast my buns and suggest you do the same. Enjoy with a cold beer.. if that is your thing!!