Place an oven safe 12-inch saucepan in the middle rack of an oven and preheat to 450 degrees, keeping the skillet in the oven until fully preheated.
In a small bowl, combine the salt and pepper and then set aside.
On a cutting board, pat the whole chicken dry with paper towels and then rub the surface with oil.
Sprinkle the entire surface of the whole chicken with the salt and pepper blend, then tie the legs back with twine and tuck the wing tips behind the back.
Transfer the whole chicken onto the now hot 12-inch saucepan, skin side up and roast the chicken until the thigh registers 135 degrees and the breast registers 120 degrees, around 25-35 minutes.
Turn off the oven and leave the chicken in the saucepan in the oven, or until the breast registers 160 degrees and the thighs register 175 degrees.
Remove the saucepan from the oven and place on the stovetop with a towel covering the hot handle.
Transfer the whole chicken to a carving board to rest, around 20 minutes.
Finally, carve the chicken and serve with the Tarragon-Lemon pan sauce.
Tarragon Lemon Sauce Directions
While the chicken rests, remove all but 1 Tbsp of fat from the skillet where the whole chicken was cooking.
Place the skillet over medium-high heat and add the diced shallot and cook until soft, around 2 minutes.
Stir in the chicken broth and mustard, using a spatula to scrape up any browned bits on the saucepan.
Cook the sauce until it is reduced, around 3 minutes.
Remove the pan from the heat and then add butter and whisk to blend.
Finally add the tarragon and lemon juice, season with salt and pepper and then set aside for serving over the chicken.