3 pounds trimmed boneless pork butt, cut into 2-inch pieces
10 thyme sprigs
6 garlic cloves, peeled and smashed
1 quart rendered pork fat, melted (see Note)
In a large bowl, toss the pork with the salt until well coated. Add the thyme and garlic and knead the garlic into the meat.
Bring the pork to room temperature. Add the melted pork fat to a pot on low with the pork and seasonings. Cover partially and cook over low heat until the meat is very tender, 4 hours, or up to 6 hours. Let cool slightly, then, using a slotted spoon, transfer the pork and garlic to a large bowl; discard the thyme. Mash the garlic and shred the pork, discarding any gristle. Stir in 1 cup of the fat and season with salt. Pack the meat into a ceramic bowl or individual crocks.
Reheat the fat and ladle a 1/2-inch-thick layer on top of the pork. Cover and refrigerate overnight. Discard the remaining fat or save it for another use.