Get grill up to 250 degrees F (120 degrees C).
For the dry rub, mix in a bowl Brown Sugar (5 tablespoon), Granulated Sugar (5 tablespoon), Sea Salt (5 tablespoon), Ground Black Pepper (1 tablespoon), Ground White Pepper (1 teaspoon), Garlic Powder (1 tablespoon), Paprika (5 tablespoon), Onion Powder (1 teaspoon), Old Bay® Seasoning (1 teaspoon), Chili Powder (1 tablespoon), and Cayenne Pepper (1 teaspoon).
Coat the meat side of the Pork Shoulder (8 pound) with Yellow Mustard (1/4 cup), and liberally spread the rub on the meat side.
With a sharp knife, make crisscrosses on the fat side of the pork. Then spread Yellow Mustard (1/4 cup) on the surface, followed by spreading dry rub on the pork shoulder.
Add 4 pieces of apple wood chunks to the coals for smoking. Set-up drip pan underneath the pork. Fill the drip pan halfway full with a mixture of equal parts apple cider vinegar and water.
Set pork on the grill, fat side up. Cook for one hour then insert two meat thermometers into pork.
Cook for about another 6-7 hours, until meat thermometers reads 200 degrees F (95 degrees C).
While pork is cooking, assemble the coleslaw. Place Green Cabbage (1/2 head), Red Cabbage (1/2 head), and Carrot (1) into a large bowl. Mix them together well.
Add the bottle of frog bone "Spanish moss" white Frog Bone "Spanish Moss" White Barbecue Sauce (12 fluid ounce) to the bowl and toss to coat. Season with Salt and Pepper (to taste).
Transfer pork on top of some foil. Wrap and rest for 30 minutes to an hour. Shred the pork with two forks after resting.
In a large saucepan, mix Apple Cider Vinegar (1 1/2 cup), Molasses (2 tablespoon), Unsalted Butter (1/2 cup), Dry Mustard (1 1/2 tablespoon), Worcestershire Sauce (1 tablespoon), Dark Brown Sugar (1 cup), Salt (1/2 teaspoon), Ground Black Pepper (to taste), and Cayenne Pepper (to taste) together.
Bring to a boil, then slowly add Corn Starch (2 teaspoon) and Water (2 teaspoon) until smooth. Stir for about a minute, then set the sauce aside to cool.
Toast your Hamburger Bun (to taste), top with shredded pork, some sauce and some coleslaw. Serve with Pickles (to taste) and enjoy!