Chop the vegetables.
Preheat oven to 450º. Adjust oven rack to middle position with no racks above it. Place large oven safe skillet on the rack.
Combine salt and pepper in a little bowl.
Rinse chicken, inside and out, with cold water and pat completely dry with paper towel.
Place the lemon, onion and tarragon inside the bird.
Rub entire surface of chicken with olive oil.
Sprinkle evenly all over with salt mixture and rub it in.
Truss the legs together with twine and tuck wing tips under the back.
In a large bowl, toss vegetables with olive oil, 1/2 tsp salt and 1/4 tsp pepper.
Transfer chicken, breast side up, to the hot skillet in the oven; place vegetables around it in the skillet. NOTE: If you cannot fit all the vegetables in the skillet, roast the remainder in a baking dish.
Roast until chicken breasts register 120º, about 40 minutes.
Remove the skillet from the oven quickly so as not to lose any heat.
Transfer vegetables to a separate dish, cover to keep warm and set aside.
Now here’s the cool part. Return the skillet with the chicken to the oven, turn off the heat and leave the chicken in the oven until breasts register 160º, about 30 minutes.
When it’s ready, transfer chicken to carving board and let rest, uncovered, for 10 minutes.
Meanwhile, as chicken rests, prepare pan sauce.
Be careful – put an oven mitt on the skillet’s handle!
Remove all but 1 tablespoon or so of the fat from the skillet.
Over medium heat, add shallot and cook 2 minutes.
Add chicken stock and Dijon. Stir to release any bits from the bottom of the pan. Cook 5 minutes.
Add tarragon and lemon juice. Taste for salt and pepper.
Carve chicken. Serve with vegetables and pan sauce over it all!