Preheat the oven to 400 degrees F. Position a rack in the center of the oven.
Arrange the pearl onions and carrots in the bottom of a roasting pan. Drizzle with the wine. Set a roasting rack in the center of the pan on top of the vegetables and brush with the oil so that the chicken doesn't stick.
Place the chicken, breast-side up, on the rack. Sprinkle the chicken all over with salt and pepper. Put the pan in the center of the oven and roast until the juices run clear or an instant-read thermometer inserted into the thickest part of the thigh (avoiding bone) registers 165 degrees F. (I calculate cooking about 15 minutes per pound of bird, so for a 4-pound bird I check the juices and temperature after 1 hour of cooking.)
Remove the chicken from the oven and allow it to rest in the pan for at least 10 minutes or up to 20.
Transfer the chicken to a cutting board, gently placing it breast-side down so the juices can flow through the breast meat as it rests for an additional 10 to 15 minutes.
Place the roasting pan with the vegetables on a burner on the stove and add the chicken stock and mustard. Simmer gently, scraping any bits of chicken fat and skin from the bottom. Let the sauce simmer a little with the vegetables, 2 to 3 minutes. Add half the butter and cook, about 1 minute. Remove the vegetables from the pan to a plate. Add the lemon juice, half the tarragon and 1 more tablespoon butter. Allow the butter to melt, then remove the gravy to a serving bowl.
Turn the chicken breast-side up on a cutting board and carve. (The cut side will need some seasoning.) Rub the remaining butter onto the carved chicken breast meat and season with salt. Sprinkle with the remaining tarragon. Serve the chicken with the sauce and vegetables on the side. |