Place the chicken breasts in the bottom of the slow cooker in a single layer.
In a bowl, stir together the honey, soy sauce, minced garlic, and chicken broth until the honey dissolves.
Pour the sauce over the chicken. Cover and cook on low for 4 hours.
After 4 hours, pour in the cornstarch slurry and stir gently around the chicken.
Add the broccoli florets on top of the chicken. Cover and cook for 30 more minutes until the broccoli is tender but still bright green.
Remove the chicken, slice or shred it, and return it to the sauce. Stir to coat.
Spoon the chicken, broccoli, and sauce over the cooked rice. Top with sliced green onions and sesame seeds.