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. (reserving one cup for the sauce)
Place back in oven, uncovered for 90 minutes more.
Remove the pork from the oven.
Tent the pork with foil for 20 minutes to let it rest.
Shred the pork apart and mix to evenly distribute fat and seasonings.
Carolina Style Mustard BBQ Sauce
Place all ingredients (except the cornstarch and water) in a saucepan and heat to med/hi
Mix the cornstarch and water in a separate bowl
Once the mixture is bubbling, stir in the cornstarch mixture for about a minute
Set aside to serve over the pulled pork