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Trim most of the fat from the exterior of the meat but not all of it. Leave no more than ¼-inch (3mm).
If you have the time, season the pork butt all over with salt and refrigerate it for 12 to 24 hours before cooking.
Just before cooking, wet the surface lightly with water and sprinkle on the Meathead's Memphis Dust.
Prepare a smoker for cooking at about 225°F (107°C) or set up a grill for 2-zone or indirect smoke cooking.
Once the smoker or grill has come to temperature, insert the probe from a digital leave-in thermometer into the pork butt.
Put the meat on the smoker (or on the indirect heat side of a grill), right on the grate and not in a pan.
Allow the pork butt to smoke uninterrupted, but be sure to check your cooker every hour or so to make sure it is maintaining temperature.
When the pork butt hits an internal temperature of about 170°F (77°C), allow it to continue cooking past this point.
When the internal temperature hits 203°F (95°C), check if the pork butt is ready.
If the pork butt is not ready, close the lid and allow it to continue cooking.
About 30 minutes before sitting down for dinner, put the meat into a large pan to catch drippings.
Pull the pork butt apart with Claws, gloved hands, or forks. Discard big chunks of fat.