Heat oil in a large skillet over medium-high heat. Brown pork for 5 minutes, turning; transfer to a 4-quart slow cooker.
Add vinegar, soy sauce, 1/3 cup water, garlic, bay leaves, and pepper. Cover; cook on low about 6 hours until pork is fork-tender and reaches at least 145°F.
During the final hour, bring rice and 1 1/2 cups water to a boil in a covered saucepan. Reduce to low; cook 40 to 45 minutes. Rest covered 10 minutes.
Transfer pork to a plate; remove bay leaves. Pour liquid into a small saucepan and skim excess fat. Simmer 5 to 8 minutes until reduced to about 3/4 cup; return pork to sauce.
Steam cabbage, covered, over simmering water for 8 to 10 minutes until tender.
Divide pork, sauce, rice, and cabbage among 4 plates. Rest cooked pork at least 3 minutes before eating.