Make the dry rub.

In a small bowl mix together all of the ingredients for the dry rub until well combined. Set aside.

Prepare the pork.

Pat the pork dry with paper towels.

Rub the meat with olive oil on all sides.

Generously coat the pork with the rub mixture on all sides, massaging the rub into the meat.

Wrap the roast in plastic wrap and refrigerate for at least 8 hours, preferably overnight.

Roast the meat.

Preheat the oven to 300 degrees.

Place the pork roast in a deep roasting pan and pour the pineapple juice around the meat.

Cover the pan tightly with aluminum foil and cook for 90 minutes.

Check the pan to ensure there is at least an inch of liquid.  If not, add more juice, water, soda, or broth.

Recover and continue to cook for another 4-5 hours, checking the liquid in the pan every 90 minutes or so.

The pork is done when it’s falling apart and an instant-read thermometer inserted into the thickest part registers 170 degrees.

Remove the pork from the oven and transfer it to a large platter.  Wrap with foil and allow to rest for about 10 minutes.

While the meat is still warm, take 2 forks and pull the meat apart to form shreds.

Pour 1 cup of barbecue sauce over the pork and mix well to coat.

Make the barbecue sauce.

In a large saucepan over medium heat, saute the onions and garlic in the olive oil until the onions just begin to turn translucent – about 4 minutes.

Add the jalapeno and ginger to the onions, stir well, and continue to cook for another 2 minutes.

Toss in the pineapple, brown sugar, dry mustard, salt, lime juice, pineapple juice, ketchup, vinegar, Worcestershire sauce, and molasses. Stir to combine.

Bring the sauce to a boil, then reduce the heat to a simmer and cook for 20-30 minutes or until the mixture has thickened and is slightly reduced.

Remove the pot from the heat and stir in the rum.

Return the pot to the heat and simmer, stirring constantly, for another 5 minutes.

Use an immersion blender to blend the mixture into a smooth sauce.

Spoon into a serving bowl.  Allow the sauce to cool to room temperature.

Store leftovers in a tightly covered container in the refrigerator for up to 1 week.