Preheat your smoker to 225°F using oak or hickory wood for an authentic Texas flavor profile.
Trim the beef brisket of excess hard fat, leaving a consistent 1/4-inch layer on the fat cap to keep the meat moist.
In a small bowl, mix the sea salt, coarse black pepper, and garlic powder to create a traditional Dalmatian rub.
Apply the rub generously to all sides of the brisket, pressing it into the meat so it adheres well.
Place the brisket on the smoker grates, fat side up, and smoke until the internal temperature reaches 165°F.
Remove the brisket and wrap it tightly in peach butcher paper to preserve the bark while tenderizing the meat.
Return the wrapped brisket to the smoker and continue cooking until the internal temperature reaches 203°F.
While the meat rests for at least 45 minutes, whisk together the apple cider vinegar, yellow mustard, and celery seed.
Toss the dressing with the shredded green cabbage in a medium bowl and refrigerate until ready to serve.
Slice the rested brisket against the grain into thin strips and serve alongside the chilled vinegar slaw.