In a large pot or dutch oven, brown chicken in 1 tablespoon olive oil (it doesn't have to be cooked through). Remove from pot and set aside.
Cook onion, carrot, celery and red pepper in 1 tablespoon olive oil for about 3 minutes or until onion is slightly softened. and 1/4 cup white wine and allow to boil to about 1 tbsp. Stir in 3 tablespoons of flour, seasonings and salt & pepper to taste. Cook over medium heat about 2 minutes.
Add potatoes, sweet potatoes, remaining white wine, browned chicken and broth. Bring to a boil, reduce heat and simmer covered for 30 minutes.
Remove lid and stir in green beans (peas) and cream. Thicken if desired (below) and simmer an additional 10 minutes uncovered.
To thicken: In a mason jar combine remaining 2 tablespoons flour and 1 cup water or broth. Shake very well (ensure there are no lumps) and add a little at a time to boiling stew to reach desired consistency.