Adjust oven rack to middle position, place 12-inch ovensafe skillet on rack, and heat oven to 450 degrees.

Combine 1 tablespoon kosher salt and ½ teaspoon pepper in bowl.

Remove giblets from 1 (3½- to 4-pound) whole chicken. Pat dry with paper towels.

Rub entire surface with 1 tablespoon extra-virgin olive oil.

Sprinkle evenly all over with salt mixture and rub in mixture with your hands to coat evenly.

Tie legs together with twine and tuck wing tips behind back.

Transfer chicken, breast side up, to preheated skillet.

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.

Transfer chicken to carving board and let rest, uncovered, for 20 minutes.

While chicken rests, remove all but 1 tablespoon of fat from now-empty skillet using large spoon, leaving any fond and jus in skillet.

Place skillet over medium-high heat, add 1 minced shallot, and cook until softened, about 2 minutes.

Stir in 1 cup chicken broth and 2 teaspoons Dijon mustard, scraping skillet bottom with wooden spoon to loosen fond.

Simmer until reduced to ¾ cup, about 3 minutes.

Off heat, whisk in 2 tablespoons unsalted butter, 2 teaspoon minced tarragon, and 2 teaspoon lemon juice.

Season with pepper to taste; cover and keep warm.

Carve chicken and serve with pan sauce.