Spray a large baking pan with cooking spray. Add potatoes, carrots, onions, vinegar, oil, garlic, 1 tsp thyme, 1 tsp rosemary, tarragon, salt and pepper. Mix well. Roast, uncovered, at 425°F for 30 minutes. Stir once, halfway through cooking time. Add green beans, and roast for 10 more minutes.

Meanwhile, pour wine into a large saucepan. Add remaining thyme and rosemary. Bring to a boil. Add chicken pieces and reduce heat to medium-high. Cook, uncovered, until chicken is cooked through, about 12 minutes.

Add roasted vegetables to chicken and wine. Stir in 2 1/2 cups broth. In a small bowl, combine fllour with remaining 1/2 cup broth and stir until lump-free. Add flour mixture to chicken and vegetables. Cook until stew is bubbly and has thickened, about 3 minutes. Serve hot.