In a bowl whisk together the teriyaki, chicken broth, brown sugar, soy sauce, chili sauce and pineapple juice. Set aside.
Put the chopped onions and carrots in a 5-quart slow cooker. Place the pork on top of the carrots and onions and pour half of the pineapple juice mixture over pork. Reserve remainder for Hawaiian sauce. Cover and cook on low for 7 to 8 hours until the pork is easily shred with a fork.
Meanwhile, make the Hawaiian sauce:
Heat the oil over medium heat in a medium saucepan. Add garlic and ginger and saute until soft, about 2 minutes.
Add the remaining pineapple juice mixture, bring to a boil, then reduce heat and simmer for 10 minutes. Remove from heat and set aside.
Serve the shredded pork on rolls drizzled with the Hawaiian sauce or on the side for dipping.