1. Place the chicken breast side down in the baking dish. Cut the potatoes into quarters. Put the potatoes, shallots and carrots around the chicken in the baking dish. Put the bay leaves between the vegetables.
2. Mix the butter, oil, wine or juice, garlic, paprika, salt (in moderation) and pepper in a bowl. Purée with a hand blender until smooth and coat the chicken and vegetables with it. Cover the chicken with plastic wrap and set in the fridge to rest for 1 hour.
3. Preheat the oven to 350°F. Remove wrap from chicken and roast until internal temperature reaches 165°F, about 1 1/2 hours, basting with pan juices after 45 minutes. Remove the chicken from the oven, cover loosely with foil and let rest for 15 minutes. Carve and serve with roast vegetables.
Per serving: 761 calories, 55g fat, 16g saturated fat, 178mg cholesterol, 197mg sodium, 33g carbohydrate, 6g fiber, 11g sugar, 35g protein