Heat a large cast-iron skillet over medium-high heat.
Rub the oil completely over the pork and season with the salt, pepper and cayenne. Brown the pork shoulder in the skillet on all sides; this will take about 10 minutes. Remove from the skillet and allow to cool slightly before rubbing with the mustard, then coating with the brown sugar.
Place the pork in a 3- to 4-quart slow cooker, then add the soda and liquid smoke. Cover and cook on low for 7 to 8 hours. When it is done, the pork will feel extremely tender when prodded.
Remove the pork from the slow cooker, then shred the meat using 2 forks and pull off the bone. Mix the meat with any remaining cooking liquid from the slow cooker. Serve with sandwich buns and toppings of your choice.