Pat the brisket dry and trim the fat cap to about ¼ inch thick. Remove any oxidized meat and large hard pieces of fat. Lightly coat all sides with paprika, then season generously with Texas-style brisket rub. Let the brisket sit at room temperature for 30–60 minutes while the smoker preheats so the seasoning can adhere.
Preheat the Traeger to 180°F. Place the brisket fat side down on the grill and insert a temperature probe into the thickest part of the flat. Cook overnight at 180°F to allow the brisket to slowly absorb smoke and begin rendering the fat.
Once the brisket reaches an internal temperature of 145–150°F, increase the grill temperature to 225°F. The brisket will likely enter the stall around 155–165°F, where the temperature stops rising for a period of time. This is completely normal and helps create a tender finished brisket. Keep the lid closed as much as possible during this stage.
When the brisket reaches about 165°F and the bark is dark and set, wrap it tightly in butcher paper. Increase the smoker temperature to 250°F to help push the brisket through the stall.
Continue cooking until the brisket is probe-tender, usually around 203–205°F internal temperature. A thermometer probe should slide into the flat with very little resistance.
Keep the brisket wrapped and rest it in a cooler or insulated container for at least 1–2 hours before slicing. Resting allows the juices to redistribute and helps ensure a moist, tender brisket.