How to Make It
Squeeze juice from 1 orange to equal ¼ cup; add to a 5- or 6-quart slow cooker. Stir in lemon juice, garlic, 4 teaspoons salt, ½ cup cilantro, and 1 teaspoon pepper. Add pork, turning to coat. Cover and cook on low until pork is fork-tender, 6 to 8 hours.
Preheat broiler to high with oven rack 6 inches from heat. Shred pork with 2 forks and spread in an even layer on a rimmed baking sheet (reserve ½ cup cooking liquid). Broil until pork is browned and crisp, about 10 minutes. Season with remaining ½ teaspoon salt and transfer to a serving platter.
Cut away peel and pith of remaining 2 oranges while pork broils. Working over a medium bowl, cut out orange segments and squeeze membranes to extract juice. Stir in cabbage, onion, oil, vinegar, and remaining ¼ cup cilantro and ¼ teaspoon pepper; toss gently to combine.
Skim off fat from reserved cooking liquid; stir into beans. Serve pork with tortillas, slaw, and beans.