Remove the corned beef brisket from its packaging and rinse it. Submerge the brisket in a large bowl of cold water and soak for 2 to 3 hours in the refrigerator, changing the water every hour to remove excess curing salt.
Preheat your smoker to 250°F, using hickory or cherry wood.
Remove the brisket from the water and pat it completely dry with paper towels.
Brush the entire surface of the brisket with mustard, then coat evenly with the pickling spice and BBQ rub.
Place the brisket directly on the smoker grates, fat side up. Smoke for 3 to 4 hours, or until the internal temperature reaches 160°F and a solid bark has formed.
Transfer the brisket to an aluminum foil pan. Pour the beef broth into the pan and add the fresh rosemary sprigs.
Cover the pan tightly with heavy-duty aluminum foil and return it to the smoker. Increase the smoker temperature to 275°F.
Continue cooking for another 2 to 3 hours, until a meat thermometer inserted into the thickest part reads between 200°F and 205°F and the meat feels tender.
Remove the pan from the smoker and let the brisket rest, still covered, for at least 30 to 45 minutes.
Transfer the brisket to a cutting board, slice against the grain, garnish with fresh parsley, and serve.