Place racks in the center and bottom third of the oven and preheat the oven to 400°F

Dry the chicken well using paper towels.

In a small bowl, mix the butter, garlic, 1 1/2 teaspoons of kosher salt, and 1/2 teaspoon of freshly ground black pepper. Remove the leaves from the rosemary stalks; place the stalks in the main chicken cavity. Finely chop the leaves and mix them into the butter mixture. Finely grate the lemon zest into the rosemary mixture.

Quarter the lemon and place it in the main chicken cavity.

Using your fingers, separate the skin from the meat of the chicken breasts. Spread 3 tablespoons of the rosemary butter evenly under the skin. Transfer the chicken to a heavy rimmed baking sheet. Rub the remaining rosemary butter all over the chicken.

Using kitchen twine, tie the chicken legs together. Roast the chicken for about 1 hour and 20 minutes, or until it is golden and an instant-read meat thermometer inserted into the thickest part of the thigh reaches 165°F.

Rest the chicken on a carving board

for 10 minutes before serving.

Meanwhile, toss the apples, sugar, and 2 tablespoons of water in an 8-inch square baking dish. Place the apples cut side down in the dish.

Bake for about 55 minutes, or until the apples are very tender. Transfer the apples to a cutting board and chop the apples to a coarse consistency. Transfer the applesauce to a serving bowl.

Carve the chicken and serve with the roasted applesauce.