Add all ingredients into a 6 quart crock pot then stir to combine. Cook on low for 8-10 hours or until pork shreds easily with a fork.
For the Cuban-Style Black Beans:
Heat oil in a large skillet over medium heat. Add bell pepper and onion, season with salt and pepper, then saute until vegetables are tender, 5-7 minutes. Add garlic then saute for one more minute. Add dried oregano, black beans, chicken broth, and vinegar then simmer until most of the broth has been absorbed and beans are tender. Taste then add salt and pepper if necessary.
Serve pork and beans over cooked Cilantro-Lime Rice (see notes), in corn tortillas, or on top of nachos.