For the pork: In a small bowl combine the salt, pepper, paprika, and ground cloves until well combined.
Dry rub the pork with the seasoning mixture and let it cure in the fridge overnight or up to 24 hours.
Preheat the oven to 300 °F and bring the pork to room temperature for about 1 hour before placing it in the oven.
Cook the pork on an aluminum lined cooking sheet for 4 hours, cover the pork butt with aluminum foil 2 hours into the cooking process. Try to open the oven as little as possible during this time.
For the sauce: Combine 12 ounces of Dr Pepper and 2 tablespoons of cornstarch in a small bowl and whisk to create a slurry. In a medium saucepan on medium heat, combine the ketchup, hot sauce, pepper, salt, remaining 12 ounces of Dr Pepper, liquid smoke, paprika, garlic powder, onion powder, mustard powder, vinegar, brown sugar, soy sauce, and the cornstarch slurry and whisk to combine.
Bring sauce to a low simmer and simmer for 30 minutes.
Remove from heat and set aside.
Pull the pork out of the oven and let it rest for 15 minutes.
Once rested, shred the pork and toss in the Dr Pepper BBQ Sauce.
In a skillet on medium-high heat, melt 1 tablespoon of butter. Place the bun’s face-side down onto the butter and toast until browned, about 1-2 minutes. Toast the bun in butter, remove from heat, add ¼ pound of pulled pork to each sandwich.