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 oil all over chicken. Sprinkle salt mixture evenly over surface of chicken, then rub mixture in with your hands to coat evenly. Tie legs together with kitchen twine and tuck wingtips behind back.
Transfer chicken, breast side up, to skillet in oven. Roast until breast registers 120 degrees and thighs register 135 degrees, 25 to 35 minutes. Turn off oven and leave chicken in oven, opening door as little as possible, until breast registers 160 degrees and thighs register 175 degrees, 25 to 35 minutes.
Using potholder (skillet handle will be hot), remove skillet from oven. Transfer chicken to carving board and let rest, uncovered, for 20 minutes.
Meanwhile, add shallot to fat left in skillet and cook over medium high heat until softened, about 2 minutes. Stir in broth and mustard, scraping up any browned bits. Simmer until reduced to ¾ cup, about 3 minutes. Off heat, whisk in butter, herbs, and lemon juice. Season with pepper to taste. Carve chicken and serve with sauce.