Heat olive oil in a large pot over medium-high heat and sear the diced chicken until golden brown. Remove and set aside.
In the same pot, sauté onions, carrots, celery, and bell pepper until soft. Stir in rosemary, thyme, sage, salt, and pepper for extra flavor.
Sprinkle 3 tablespoons of flour over the veggies, stirring well to coat. Cook for a minute to eliminate the raw flour taste.
Pour in white wine to deglaze the pot, scraping up the browned bits for deeper flavor.
Add chicken broth, potatoes, sweet potatoes, and seared chicken, then bring to a boil. Reduce heat and let simmer for 25 minutes.
Stir in green beans (or peas) and let cook for another 5 minutes until all veggies are tender.
In a small bowl, mix the remaining 2 tablespoons of flour with heavy cream to form a slurry, then stir it into the stew for a creamy finish.
Let the stew thicken for 2-3 minutes, then serve hot with crusty bread or mashed potatoes. Enjoy!