In a small bowl, combine 2 tablespoons olive oil, cumin, oregano, salt, and fresh ground black pepper and stir to create a paste. Rub the paste all over the trimmed pork shoulder. Heat the remaining oil in a large heavy skillet or Dutch oven over MEDIUM-HIGH heat. Sear the pork until it forms a browned crust on both sides. Transfer the pork roast to your slow cooker.
Pour the chicken broth, orange, and lime juice over the pork roast in the slow cooker. Sprinkle with the minced garlic and tuck a bay leaf down into the liquid. Cover and dook on LOW for 6-8 hours, or until you can easily shred the meat with a fork. Remove and discard the bay leaf and shred the meat into the cooking juices.
Meanwhile, prepare the Easy Cuban-Style Black Beans.
Prepare the rice according to package directions, using chicken or vegetable broth in place of water.
Serve shredded pork with Easy Cuban-Style Black Beans and rice.