Preheat a smoker to 225 degrees F (107 degrees C) according to manufacturer's instructions. Maintain temperature for 15 to 20 minutes.
Combine pepper, paprika, and garlic powder in a bowl; add the spice packet from the brisket and mix well. Generously sprinkle the spice mixture over both sides of the brisket.
Drain wood chips and place on coals. Place a water pan on the smoker and add water to the depth of the fill line. Place brisket on the lower cooking grate and cover with the smoker lid.
Smoke brisket, maintaining the smoker's internal temperature at 225 degrees F (107 degrees C) until an instant-read thermometer inserted into the thickest part registers at least 190 to 200 degrees F (88 to 93 degrees C), 4 to 6 hours.
While the brisket is cooking, prepare coleslaw. Combine mayonnaise, sugar, lemon juice, vinegar, pepper, and salt in a medium bowl; whisk until smooth.
Cut each cabbage into quarters and remove the core. Thinly slice cabbage quarters and transfer to a large bowl. Pour mayonnaise dressing over top and mix well with your hands. Cover with plastic wrap and refrigerate until ready to serve.
Remove brisket from the smoker and let rest for 40 minutes. Slice corned beef against the grain.