The day prior to smoking brisket, trim. Using a sharp knife, remove excess layers of fat and silver skin.
Coat the brisket with olive oil and then combine the dry rub ingredients in a bowl. Reserve 1/3 of a cup for the burnt ends. Liberally season the brisket with the dry rub. Don't be shy. Wrap in foil and place in fridge until ready to cook.
Preheat smoker to 250 degrees F using apple or cherry wood. Remove the brisket from the fridge at this point.
When smoker is at temp, insert your meat thermometer into the flat and place in smoker. We place ours fat cap side down, as the bottom of our smoker is hotter than the top.
Smoke until the brisket reaches an internal temperature of 165 degrees F. Remove from smoker and then, using a sharp knife, remove the point from the flat. Trim some of the excess fat off point and the flat.
For the Brisket Flat
Wrap the flat in peach butcher paper, and then re-insert the meat thermometer. Place back in smoker and continue to cook until the internal temperature of the brisket flat reaches 190 degrees. Begin temping the flat in various places, and remove from smoker when the temperature probe inserts easily into the flat like butter. This can take 3 to 5 additional hours depending on size of brisket.
Place wrapped brisket flat in a cooler with no ice and let rest for an hour. Remove and then slice against the grain.
For the Burnt Ends
After placing the flat into smoker, cut the point into 1 1/2-inch cubes. Place into a smoker safe tray. Season with the reserved 1/3 cup of dry rub, and then add barbecue sauce, butter and honey, and toss together. Place uncovered in the smoker and stir once the butter and honey have melted.
Smoke in the tray uncovered for 2 hours. Stir midway to incorporate the sauce and move the cubes around. After 2 hours cover with foil and place back into the smoker. Remove when the internal temperature ranges from 190 to 205, or when the meat thermometer inserts into the cube like butter (expect an additional 1 or 2 hours).