Preheat your oven to 350°F (175°C).
Heat the vegetable oil in a large skillet over medium-high heat. Add the chicken pieces and brown on all sides. Remove the chicken and set aside.
In the same skillet, add the chopped onion and cook until softened, about 5 minutes.
Stir in the minced garlic and cook for another minute.
Add the sliced carrot, cubed potatoes, and chopped bell pepper. Cook for about 5 minutes, stirring occasionally.
Return the browned chicken to the skillet. Add the green beans, chicken broth, coconut milk, soy sauce, fish sauce (if using), ground paprika, dried thyme or rosemary, salt, and black pepper.
Stir everything well and bring to a simmer.
Tear off large pieces of banana leaves or aluminum foil. Spoon a portion of the chicken and vegetable mixture onto the center of each leaf or foil. Wrap tightly to form a secure packet.
Place the wrapped packets on a baking sheet or in a baking dish.
Bake in the preheated oven for 45-60 minutes, or until the chicken is fully cooked and tender.
Carefully unwrap the packets and serve the Mumu hot.
Enjoy your meal!