Combine pork roast, sea salt, garlic and ½ pound Havarti cheese in a slow cooker.
Cook on high for 1 hour, then 8 hours on low.
Shred with two forks and keep warm in slow cooker.
Make Hawaiian barbecue sauce.
In a small saucepan over medium heat, combine pineapple juice, vegetable oil, molasses, soy sauce, ginger and garlic.
Bring to a simmer, then reduce heat to keep warm.
Build sandwiches.
Lay bread on cutting board and spread butter on 1 side of each slice.
Flip 6 slices over so butter side is down and layer each with 1 slice of Havarti cheese, 1 scoop pulled pork, a drizzle of Hawaiian barbecue sauce, 1 grilled pineapple slice and a second slice of Havarti cheese.
Cap each sandwich with remaining bread slices, butter side up.
Working in batches, cook sandwiches in a large skillet over medium-low heat.
Place butter side down in skillet and cook, flipping intermittently, until cheese is melted and bread is golden brown on both sides.