Preheat oven to 300 degrees.
In a small bowl mix dijon mustard, garlic, brown sugar, salt, black pepper, and paprika.
Pat dry pork butt/shoulder with paper towel. Rub pork all over with mustard seasoning mixture.
Heat a skillet over high heat. Add butter and oil. Once hot, carefully add the pork to the skillet and sear for about 30 seconds on each side.
Transfer pork to an oven safe dish. Pour apple cider vinegar and broth around the pork. Cover dish with foil.
Bake for about 2 1/2 - 3 hours until pork is fork tender. Internal temperature should be at least 145 degrees. When done, remove from oven and let rest for at least 5 minutes before slicing and serving.
In a small bowl, whisk all ingredients to make the honey dijon sauce.
Slice pork into 1/4"- 1/2" slices and serve with a drizzle of the honey dijon sauce. Enjoy!