You'll rely on this hearty chicken dinner again and again. Total time to prepare, about 1 hour and 15 minutes, most of that is unattended cooking time.
1. Preheat oven to 450 degrees. In a 5-qt dutch oven or heavy pot, combine 1-1/2 cups low sodium chicken broth and 1/3 cup dry white wine. Rinse and pat dry a 3-4 lb whole chicken, then rub the chicken, all over, with one tablespoon of room temperature unsalted butter and season generously with coarse salt and ground pepper. Tie legs together with twine. Place chicken in pot and bake uncovered for about 30 minutes.
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Remove the pot from the oven and add the vegetables. Bake until chicken juices run clear when pierced between breast and leg or an instant-read thermometer inserted in thickest part of the thigh (avoiding bone) registers 165 degrees, about 35 to 45 minutes. Let chicken rest 10 minutes.
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3. Meanwhile, set a steamer basket in a large pot filled with 2 inches boiling water. Place 1 pound new potatoes, halved or quartered (if large) in basket, cover, and steam until tender, about 15 minutes. Season with coarse salt and pepper.