1Add the first 7 ingredients to a large slow cooker and cook on low for 10 hours. Let it cool for a couple hours and then move slow cooker insert into the refrigerator with lid askew to allow for air to flow from the top. Refrigerate overnight. When ready to serve use a large spoon to scoop off all of the fat hardened on the surface.
2Remove pork and slice into ½-inch slices against the grain.
3Transfer remaining juices to a medium sauce pan and bring to a low simmer.
4To build the sandwiches spread mustard on both sides of an open roll Build the sandwich in the following order: slices of cheese, slices of pork with a bit of the sauce drizzled on top, slices of boiled ham, more slices of pork and sauce, pickles, and more cheese.
5Heat a cast iron pan on medium-low heat and add a sandwich. Place something heat-proof and heavy on top of the sandwich (like another cast iron pan). Cook for 4 to 5 minutes and then, using a spatula, flip the sandwich over, place the heavy object back on top and cook for another 4 to 5 minutes.
6Use the remaining juice as a dip for the sandwiches.