Preheat oven 300.
Using a paring knife, create 6, 2-inch deep holes fairly evenly spaced through the meat. Push a peeled clove of garlic into each hole until no longer visible.
Sprinkle the pork evenly with salt.
In a small bowl mix together the brown sugar, pepper, paprika, chili powder, and onion powder. Rub the spiced all over the surface of the pork.
In a large oven safe pot or Dutch oven (with an oven safe lid) heat the oil until hot but not smoking. Sear the meat on all sides, about 3 minutes per side.
Add the beer and broth, bring to a simmer.
Cover and place in the oven. Turn the meat over every 30-45 minutes. If the pot begins to dry out, add extra broth or hot water. Allow to cook until meat is falling apart, about 3 to 4 hours.
Remove from oven, shred using two forks while still in the pot. Allow to sit in the pan juices for ten minutes while you prepare the jalapeno slaw. Remove meat from pan juices, draining off most of the liquid prior to serving.
To make the slaw, combine all the jalapeno slaw ingredients in a bowl, toss to coat. Fill each sandwich bun with pork topped with slaw.