Heat the pot with 1 tablespoon olive oil and brown the diced chicken thighs over high heat. You don’t need to cook them through—just get a nice caramelized surface for flavor. Remove the chicken and set aside.
Add the remaining oil, then cook the chopped onion, carrot, and celery until the onion softens (about 3 minutes). Stir in 3 tablespoons of the flour, plus the herbs, salt and pepper, and let the flour cook for about 2 minutes to eliminate the raw taste.
Stir in the diced potatoes, sweet potatoes, red bell pepper, white wine, browned chicken and chicken broth. Bring to a boil, then reduce heat, cover, and simmer for 30 minutes.
Remove the lid, stir in the green beans (or thawed peas) and the heavy cream. If you’d like a thicker stew, mix the remaining 2 tablespoons of flour with 1 cup water or broth to make a slurry and gradually add it while stirring. Simmer uncovered for another 10 minutes.