In a large pot, combine 4 quarts water, 1 C salt, 1/2 C brown sugar and 3 tbsp liquid smoke.
Place the pork in the brine and cover.
Chill in the refrigerator for 2 hours.
Preheat oven to 350 degrees F.
Remove the pork from the brine and pat dry with paper towels.
In a small bowl, combine 2 tbsp mustard, 2 tbsp Dijon, 1 tbsp liquid smoke and 1 tbsp honey.
Cover the pork on all sides with the mustard mixture.
In another small bowl, combine the 2 tbsp brown sugar, 1 tsp salt, 2 tbsp smoked paprika, 1/2 tsp cayenne and 1/2 tsp freshly ground black pepper.
Cover the pork with the dry rub mixture on all sides.
Place the pork, fat side up on a rimmed baking sheet that has been covered in foil and fitted with a rack.
Place a piece of parchment paper on top of the pork to cover and tightly cover the entire pan with foil.
Bake in oven for 3 hours.
Remove from oven and drain off excess juice.
Place back in oven, uncovered for 90 minutes more.
At this time, place the potatoes on the bottom rack of the oven to bake.
Remove the pork and the potatoes from the oven.
Tent the pork with foil for 20 minutes to let it rest.
Slice the potatoes in half, lengthwise and scoop out the middles.
Reserve the scooped out potatoes for another recipe.
Brush the inside of the potato skins with oil or melted butter and place on a baking sheet, cut side up.
Place under the broiler on high for 2 to 3 minutes until crisp around the edges.
Shred the pork apart and mix to evenly distribute fat and seasonings.
Top each of the potato skins with some of the pork (per your preference), a drizzle of bbq sauce and cheese.
Melt the cheese on the skins under the broiler on high for 1 minute.
Top with sour cream and chives to taste.
Carolina Style Mustard BBQ Sauce
Place all ingredients in a mason jar.
Cover with a lid and shake vigorously to combine.