In a slow cooker, combine the cubed chicken, bell pepper, onion, salt, pepper, garlic, ginger, coconut aminos, fish sauce, broth, red curry paste and lime zest. Stir until well combined. Cover and cook on low for 4 to 6 hours, or until the chicken is cooked through and tender.
In a small bowl, whisk together the coconut milk and tapioca flour until well combined. While stirring, slowly pour the mixture into the crockpot until well combined.
Stir in the green bean pieces, cover and continue to cook on low until the sauce thickens and the green beans are tender, 20 to 30 more minutes.
To finish, stir in the cilantro and basil. Serve over rice, if desired, and with a wedge of lime!