We prefer to use a 3.5 to 4-pound chicken for this recipe. If roasting a larger bird, increase the time when the oven is on in step 2 to 35 to 40 minutes. Cooking the chicken in a preheated skillet will ensure that the breast and thigh meat finish cooking at the same time.
1. Adjust oven rack to middle position, place 12-inch ovensafe skillet on rack, and heat oven to 450 degrees. Combine salt and pepper in bowl. Pat chicken dry with paper towels. Rub entire surface with oil. Sprinkle evenly all over with salt mixture and rub in mixture with hands to coat evenly. Tie legs together with twine and tuck wing tips back.
2. Transfer chicken, breast side up, to preheated skillet in oven. Roast chicken until breasts register 120 degrees and thighs register 135 degrees, 25 to 35 minutes. Turn off oven and leave chicken in oven until breasts register 160 degrees and thighs register 175 degrees, 25 to 35 minutes.
3. Transfer chicken to carving board and let rest, uncovered, for 20 minutes. While chicken rests, prepare pan sauce, if using. Carve chicken and serve.
While chicken rests, remove all but 1 tablespoon of fat from now-empty skillet (handle will be very hot) using large spoon, leaving any fond and jus in skillet. Place skillet over medium-high heat, add shallot, and cook until softened, about 2 minutes. Stir in broth and mustard, scraping up any browned bits. Simmer until reduced to 3/4 cup, about 3 minutes. Off heat, whisk in butter, tarragon, and lemon juice. Season with pepper to taste; cover and keep warm. Serve with chicken.