Sort and wash beans, and place in a large Dutch oven. Cover with water to 2 inches above beans; bring to a boil, and cook 2 minutes. Remove from heat; cover and let stand 1 hour. Drain beans, and discard liquid. Combine beans, 2 quarts water, 1 1/2 teaspoons thyme, garlic halves, and 2 bay leaves in a Dutch oven; bring to a boil. Partially cover, reduce heat, and simmer 1 hour or until almost tender. Drain bean mixture in a colander over a bowl, reserving 2 cups liquid. Discard 2 bay leaves.
Preheat oven to 350°.
Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add chicken; cook 4 minutes, browning on all sides. Remove chicken from skillet. Add 1 1/2 teaspoons thyme, carrot, onion, 1/8 teaspoon cinnamon, and minced garlic; sauté 5 minutes or until tender.
Layer half of beans in the bottom of the Dutch oven. Add the carrot mixture, chicken, and remaining beans. Add the reserved 2 cups cooking liquid, 1 teaspoon salt, 1/4 teaspoon pepper, and 2 bay leaves. Cover and bake at 350° for 1 1/2 hours or until chicken and beans are tender, spooning cooking liquid over beans occasionally. Remove from oven; discard bay leaves.
Combine 1 tablespoon olive oil, 1/8 teaspoon cinnamon, chopped parsley, and breadcrumbs, and toss the parsley mixture well. Sprinkle the parsley mixture over the chicken and beans. Broil for 2 minutes or until chicken is lightly browned.
Note: Each serving provides 405 micrograms of folate.