In a heavy-bottomed pot or Dutch oven, heat 1 tablespoon of olive oil and sear the chicken pieces until browned; full cooking is not necessary. Transfer the chicken to a separate dish and reserve. In the same pot, cook the onion, carrots, and celery in the remaining oil for approximately 3 minutes or until the onion softens slightly. Incorporate 3 tablespoons of flour along with rosemary, thyme, sage, salt, and pepper. Stir continuously over medium heat for about 2 minutes. Add the diced potatoes, sweet potatoes, bell pepper, white wine, reserved chicken, and broth. Raise the heat to bring the mixture to a boil, then lower it and let it simmer with the lid on for 30 minutes. Remove the cover, then stir in the green beans and cream. If a thicker consistency is preferred, mix the remaining 2 tablespoons of flour with 1 cup of water or broth in a tightly sealed mason jar. Shake until smooth and lump-free, then gradually introduce this slurry into the simmering stew, allowing it to thicken to the desired texture. Continue to simmer uncovered for an additional 10 minutes before serving.