How to Make It
Combine first 4 ingredients and 1/2 teaspoon each of the salt and pepper in a 5- to 6-quart slow cooker. Cover and cook on LOW 6 hours.
Sprinkle chicken with 1/2 teaspoon each of the salt and pepper. Heat 1 tablespoon of the oil in a large skillet over medium-high; add chicken, and cook until golden, 2 minutes per side. Nestle chicken into beans in slow cooker at the end of the 6-hour bean cook time. Cover; cook until chicken and beans are tender and done, about 2 hours. Transfer chicken to a cutting board; remove meat from bones and shred. Remove 3 cups of beans; drain. (Save remaining beans for another use.) Let chicken and beans cool.
Squeeze juice from 1 orange to equal 1/4 cup. Peel remaining 2 oranges; cut into segments. Whisk together orange juice, vinegar, shallots, and remaining 1/2 teaspoon salt and 1/4 teaspoon pepper in a large bowl. Add remaining 1/2 cup oil in a steady stream, whisking until incorporated. Add spinach, shredded chicken, beans, orange segments, almonds, and cheese, and toss with the dressing.