In a dutch oven or large pot, melt the butter. Add the onions, carrots, and celery then season the vegetables with salt and pepper. Stir and cook until the vegetables are softened and tender, about 5-8 minutes. Stir in the garlic.

Toss the vegetables in flour and stir until coated.

Add chicken, potatoes, red pepper, thyme, and bay leaf, then pour in the broth. Season the mixture with salt and pepper. Bring the mixture to a simmer and cook until the chicken is cooked through with no pink in it and the vegetables are tender (25-30 minutes). Stir in the green beans during the last 10 minutes of cooking.

Remove from the heat. Take out and discard the bay leaf and thyme stems. Using tongs, remove the chicken. Shred it using 2 forks, then return it to the pot. Stir the mixture to combine.

Garnish with thyme and parsley if desired, then serve.