Adapted from The Kitchen Detective: A Culinary Sleuth Solves Common Cooking Mysteries with 150 Foolproof Recipes by Christopher Kimball, (Boston Common Press, 2003).
If you purchase kosher chicken breasts, you should skip the brine, as these chickens are already salted. If using canned chicken broth, choose a low-sodium brand, or the sauce will be too salty.
For the Chicken:
For the Sauce:
For the chicken: Dissolve the salt and sugar in 2 quarts cold water in a large bowl. (You can also use a large freezer bag.) Immerse the chicken in the brine and refrigerate until fully seasoned, about 1 hour. Remove the chicken from the brine and rinse well under cold running water. Dry thoroughly inside and out with paper towels. Adjust an oven rack to the center position and heat the oven to 350 degrees.
Using a sharp knife, make three diagonal slashes in the skin of each piece of chicken, being careful not to cut into the meat. Season both sides with pepper. Meanwhile, add the olive oil to a heavy-duty 12-inch skillet over medium-high heat, and when the oil just starts to smoke, add the chicken breasts, skin-side down, and stand back - they will splatter. Cook for 7 to 8 minutes or until dark brown. Turn the breasts skin-side up and place the skillet in the heated oven. Cook for 15 to 25 minutes or until an instant-read thermometer reads 165 degrees at the thickest part of each breast. Carefully remove the pan from the oven (the handle will be VERY hot). Transfer the chicken to a warm platter and cover with aluminum foil to retain heat.
For the sauce: Pour off all but 1 tablespoon of fat from the skillet and place the skillet over high heat. Add the shallot, sherry, and chicken stock and scrape the browned bits from the bottom of the pan. Cook at a vigorous boil until the liquid has thickened slightly and has reduced by about two thirds, about 5 minutes. Add the mustard and thyme and cook 1 minute. Add the lemon juice and parsley and cook 30 seconds more. Serve immediately spooned over the chicken breasts.