Boil cider in a medium saucepan until it’s reduced by at least half, about 15 minutes. Whisk in the maple syrup, mustard, and butter. Let cool while you preheat the oven and prepare the chicken. Reserve about half of the sauce for serving at the end. Use the other half of the sauce to baste the chicken during the final 30 minutes of roasting.
ROAST THE CHICKEN
Allow chicken to sit on the counter for about 30 minutes to come to room temperature. Preheat oven to 425°F. Lightly coat the bottom of a Dutch oven with vegetable oil.
Pat chicken dry with paper towels. Season the inside cavity of the chicken liberally with salt and pepper. Stuff cavity with onion, apple, thyme sprigs, rosemary sprigs, and garlic cloves. It’s okay if you can’t fit everything in there – just stuff as much in as you can! Tie the legs together with kitchen twine and tuck the wings underneath the bird. Place the chicken (breast-side up) in the Dutch oven. Drizzle or brush the melted butter over the outside of the chicken. Season liberally all over with salt and pepper.
Roast the chicken uncovered at 425°F for 1 ½ hours, or until the juices run clear when you cut between a leg and thigh and the temperature on a meat thermometer inserted into the thickest part of the thigh reaches 170-175°F. Baste the chicken with the cider glaze after the first hour. If the skin starts to get too dark at any point, cover the pot with the lid for the remainder of the roasting time.
Remove chicken from the pot and allow to rest for 10-15 minutes before carving. Serve with reserved sauce for dipping or drizzling, if desired.