Layer the potatoes, carrots, celery, and onion in the bottom of your slow cooker. Add the chicken pieces on top.
Sprinkle the garlic, rosemary, thyme, salt, and pepper over the chicken and vegetables. Tuck in the bay leaves.
Pour the chicken broth over everything. Cover and cook on LOW for 6-7 hours or HIGH for 3-4 hours, until chicken is cooked through and vegetables are tender.
About 30 minutes before serving, stir in the frozen peas and green beans.
In a small bowl, whisk together the flour and cold water until smooth. Slowly stir this mixture into the stew to thicken it up.
Cover and cook on HIGH for another 20-30 minutes until the stew has thickened nicely. Remove bay leaves before serving. This stew stores beautifully in the fridge for up to 5 days!