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Step 1
Preheat oven to 425 degrees F.
Step 2
Remove the neck and giblets from the whole chicken, rinse with cold water and pat dry with paper towels. Place in a roasting pan and season the inside of the chicken with 1/2 teaspoon of the kosher salt and 1/2 teaspoon of the freshly ground black pepper. Stuff the chicken with the onion, celery, carrot and 6 garlic cloves. Truss legs with cooking twine and tuck wings under bird.
Step 3
In a small bowl, mix the butter, the remaining kosher salt and black pepper and the tarragon until blended. Gently work your fingers under the skin of the chicken breasts and rub half of the butter mixture under the skin, then rub the rest of the butter over the top of the chicken skin.
Step 4
Scatter the remaining garlic cloves around the chicken and pour the wine or sherry into the pan.
Step 5
Roast the chicken for 30 minutes or until the breast is firm and just beginning to brown in spots. Using tongs, turn the chicken breast-down, baste with juices and roast for 20 minutes longer, until the skin is lightly browned.
Step 6
Using tongs, turn the chicken breast-side-up and baste again. Add a ½ cup of water if the pan is looking dry. Roast for about 20 minutes longer, or until an instant-read thermometer inserted in the inner thigh registers 160° to 165° and juices are running clear.
Step 7
Transfer the bird to a cutting board and tent with foil. Carve the chicken and serve with the roasted garlic.