Place the pork shoulder roast into a large plastic bag, pour 1 cup of root beer over the meat, and squeeze out all the air from the bag. Seal the bag closed, and refrigerate 6 hours to overnight.

Mix together the light brown sugar, kosher salt, black pepper, paprika, dry mustard, onion powder, garlic salt, celery salt, cinnamon, ginger, and nutmeg in a bowl.

Remove the meat from the marinade, and shake off the excess. Rub the meat all over with the spice mixture, wrap in plastic wrap, and refrigerate for 30 minutes to 2 hours.

Mix together the balsamic vinegar, 1 1/2 cups of root beer, whiskey, and brown sugar in a bowl, and stir until the sugar dissolves.

Heat the olive oil in a skillet over medium-high heat, and sear the meat on all sides until the meat develops a brown crust, about 3 minutes per side.

Place the seared meat into a slow cooker. Pour the balsamic vinegar-root beer mixture over the meat, set the slow cooker to High, and cook for 6 to 8 hours.

Remove the roast from the slow cooker, and shred with 2 forks. Discard the bones and all but 1 cup of the liquid in the slow cooker.