Step 1

Preheat oven to 350°F. Coat a small roasting pan or a 12-inch ovenproof skillet with cooking spray.

Step 2

Combine 1 Tbsp. oil, chopped thyme, garlic, salt, and pepper in a small bowl; set aside.

Step 3

Place chicken on a large plate or plastic cutting board. Remove the neck, giblets, and liver from the cavity. (Reserve the liver for another use.) Pat the neck and giblets dry and place in the prepared pan. Top with thyme sprigs.

Step 4

Pat the chicken cavity and surface thoroughly dry with paper towels. With your fingers, separate the skin on the chicken breast from the meat, taking care not to tear the skin. Gently spread the thyme mixture under the skin of the breast. Rub or brush the remaining 1 Tbsp. oil over the entire chicken. Tuck the wing tips under the back and tie the legs together with butcher's twine. Rest the chicken, breast-side up, on the neck and giblets in the prepared pan.

Step 5

Roast the chicken until an instant-read thermometer inserted into the thickest part of the breast and thigh registers 165°F and the juices from cavity are clear, 1 to 1¼ hours.

Step 6

Transfer the chicken to a clean cutting board and set the neck and giblets aside; discard the thyme sprigs. Cover the chicken loosely with foil and let rest for about 15 minutes.

Step 7

Meanwhile, pour the drippings from the pan into a small fat separator, bowl, or measuring cup; place in the freezer to solidify the fat. Return the neck and giblets to the pan. Place the pan over medium-high heat and pour in cider. Bring to a simmer, stirring to scrape up any browned bits. Simmer vigorously for 1 minute. Add broth and return to a simmer. Simmer vigorously for 5 minutes. Discard the neck and giblets. Pass the sauce through a fine strainer into a small saucepan. Skim and discard fat from the chilled drippings (see Tip). Add the dripping juices to the sauce and bring to a simmer. Combine cornstarch and water and add to the pan; cook, whisking constantly, until slightly thickened. Add mustard and whisk to blend.

Step 8

Remove the twine and carve the chicken, discarding the skin. Serve with the gravy.