How to Make It
Preheat oven to 475°F. Season chicken with ¾￼ teaspoon salt and ￼½ teaspoon pepper. Heat oil in a large oven-safe skillet over medium-high. Add chicken, skin side down, and cook, turning once, until golden brown on both sides, 10 to 12 minutes. Transfer chicken to a plate.
Add shallots to skillet and cook until browned, about 5 minutes. Add rosemary, garlic, and broth and bring to a boil. Return chicken to skillet, skin side up. Transfer to oven and roast until chicken is cooked through and shallots are tender, 15 to 20 minutes.
Transfer chicken to a plate. Place skillet over medium-high; add beans and remaining ½ teaspoon salt and ￼¼ teaspoon pepper. Simmer until sauce is thickened and beans are crisp-tender, 3 to 4 minutes. Stir in butter. Serve chicken with vegetables and sauce.