If using a whole pork butt or shoulder, cut meat into 4-6-inch long and approximately 3-inch wide strips. If using the boneless ribs, cut them in half. Set aside.
Combine chicken broth, garlic salt and pepper in a 5 to 6-quart slow cooker. Add the pork and stir. Cover and cook until fork-tender, 6-7 hours on low (depends on the heat of your slow cooker). (See “Notes” below for instant pot method.) Drain the pork and discard the liquid.
When pork is cool enough to handle, shred the meat into bite-size pieces, with your fingers, discarding any fat. Return meat to slow cooker or a storage container (if making ahead).
Combine all sauce ingredients in a medium-size saucepan over medium-high heat. Bring to a boil, then reduce to a steady simmer. Continue to cook for about 10 minutes, stirring occasionally until liquid is thickened and starting to become syrupy. Remove rosemary stems.
Combine half of the sauce with the shredded pork. Taste and season with kosher salt and pepper, if needed. Save the rest of the sauce to drizzle on the pork when serving. Pork can be made ahead and warmed in the slow cooker before serving. Meat also freezes well. Thaw and warm before serving.