Trim the excess fat from the beef brisket, leaving about a quarter-inch cap for moisture.
In a small bowl, combine the coarse black pepper, sea salt, garlic powder, and onion powder to create the Texas-style dry rub.
Generously coat all sides of the brisket with the dry rub, pressing it into the meat to ensure it adheres.
Preheat your smoker to 225°F using oak or hickory wood. Place the brisket on the grates and smoke until the internal temperature reaches 165°F.
Wrap the brisket tightly in peach butcher paper or foil and return it to the smoker until the internal temperature reaches 203°F and the meat is probe-tender.
Remove the brisket from the smoker and let it rest for at least 1 hour in a cooler or warm oven to allow the juices to redistribute.
While the meat rests, whisk together the apple cider vinegar, Dijon mustard, and raw honey in a medium bowl.
Add the shredded green cabbage and carrots to the dressing, tossing well to combine into a bright, crunchy slaw.
Slice the rested brisket against the grain into pencil-thin slices.
Serve the warm, smoky brisket alongside the chilled vinegar slaw for a balanced, clean-eating Texas meal.