For the chicken:
1 1/2 cups kosher salt
1 whole chicken (3 1/2 to 4 pounds), cut into 8 pieces
ground black pepper
1 teaspoon vegetable oil
For the sauce:
1 large shallot, minced (about 4 tablespoons)
3/4 cup low-sodium chicken broth
1/2 cup dry vermouth
2 sprigs fresh thyme
3 tbsp. unsalted butter, cut into 3 pieces
salt and ground black pepper
1. Dissolve salt in 2 1/2 quarts cold tap water in large container or bowl; submerge chicken pieces in brine and refrigerate until fully seasoned, about 30 minutes. Rinse chicken pieces under running water and pat dry with paper towels. Season chicken with pepper.
2. Adjust oven rack to lowest position and heat oven to 450 degrees F.
3. Heat oil in heavy-bottomed 12-inch ovenproof skillet over medium-high heat until beginning to smoke, about 3 minutes; swirl skillet to coat evenly with oil. Brown chicken pieces skin-side down until deep golden, about 5 minutes; turn chicken pieces, and brown until golden on second side, about 4 minutes longer. Turn chicken skin-side down and place skillet in oven. Roast until juices run clear when chicken is cut with paring knife, or thickest part of breast registers about 160 degrees on instant-read thermometer and thickest part of thighs and drumsticks registers about 175 degrees. Using potholder or oven mitt to protect hands from hot skillet handle, remove pan from oven. Transfer chicken skin-side up to platter, and let rest while making sauce.
4. Still using potholder or oven mitt, pour off most of fat from skillet, add shallot, then set skillet over medium-high heat; cook, stirring frequently, until shallot softens, about 1 ½ minutes. Add chicken broth, vermouth, and thyme; increase heat to high and simmer rapidly, scraping skillet bottom with wooden spoon to loosen browned bits. Simmer until slightly thickened and reduced to about 2/3 cup, about 6 minutes. Pour accumulated chicken juices into skillet, discard thyme, and whisk in butter one piece at a time. Season sauce to taste with salt and pepper. Return chicken pieces skin-side up to skillet; simmer to heat through, about 1 minute. Serve immediately.
*From America's Test Kitchen