Preheat the smoker to 250 degrees. Add water to the water bowl and stir in some extra paprika and chili powder, for added flavor and moisture.
At least 40-45 minutes prior to starting, soak the wood chips in water for 30 minutes. Then, set them out on a paper towel to completely dry out.
Remove any large fat caps off of the pork butt. Season the pork with salt and pepper. Then, rub the mustard on all sides. Season with the rub blend and press into the pork.
Place the thermometer into the pork butt and set that on the middle rack in the smoker. Close the lid and let it set for 3-4 hours (60-90 minutes per pound), until the internal temperature reaches 200 to 205 degrees.
When the pork starts to get closer to 200 degrees, take a handheld thermometer and check the other areas, to make sure they are near the same temperature. While doing this, baste the pork with some of the water in the water bowl, to keep it from drying out.
Take the pork out and let it rest for 30 minutes. Then, pull the meat off the bone and shred with two forks. Add BBQ sauce and toss to coat.