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.
See Café Tips above in the post for more detailed instructions and tips.
To make in the instant pot, add chicken broth and garlic salt to the IP pot, add the pork and stir. Set instant pot to high-pressure setting and cook for 35 minutes. Allow pressure to release naturally, then drain the pork and discard the liquid. Proceed with step #3 in the recipe directions.