Place the chicken breasts in the bottom of the slow cooker.
In a small bowl, stir together the honey, soy sauce, minced garlic, and black pepper until smooth.
Pour the honey mixture over the chicken, then add the chicken broth and rinsed rice.
Cover and cook on low for 5 to 6 hours, until the chicken is tender and the rice has absorbed most of the liquid.
Remove the chicken, shred it with two forks, and return it to the slow cooker. Stir gently to combine everything.
Spoon the mixture into bowls and top with sliced green onions and sesame seeds before serving.