Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove the chicken and set aside.

In the same pot, melt the butter over medium heat. Add the carrots, celery, and onion, and sauté until softened, about 5 minutes. Add the garlic and cook for 1 minute, stirring frequently.

Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.

Stir in the rosemary, thyme, sage, bay leaf, salt, and pepper. Add the diced potatoes and return the chicken to the pot.

Pour in the white wine, scraping the bottom of the pot to deglaze and release any browned bits. Let the wine simmer for 2-3 minutes.

Add the chicken broth and bring the mixture to a boil. Reduce the heat to low, cover, and simmer for 20 minutes, or until the potatoes are tender.

Stir in the green beans and cook for an additional 5 minutes, uncovered, until the beans are tender but still bright green.

Remove the bay leaf, then stir in the heavy cream. Simmer for 2-3 minutes to heat through. Taste and adjust seasoning if needed. Serve hot and enjoy!