Remove neck, giblets, and any glaze/sauce packets from the cavity of the duck, reserving giblets and neck for another use—like making duck stock. If the duck has a pop-up timer, remove it and discard. Carefully rinse duck (avoid splashing!), inside and out, and pat dry with paper towels. Remove any excess fat or fat pads that you can easily get to without damaging the skin. Cover with plastic wrap and keep at room temperature for 30 minutes.
Position your oven rack in the lower third of your oven; preheat oven to 500°F. While the oven preheats, sprinkle 1 tsp. each of salt and pepper around the cavity of the duck. Place the onion and the fresh herbs through the thyme sprigs into the cavity. Truss the legs to the tail with kitchen twine. Pin the neck flap to the back with toothpicks and tuck the wing tips under the back (I sometimes break the joint in the wings so that they tuck under more easily). Salt and pepper the outside of the duck liberally.
Place the duck, breast side down, onto a rack set in a shallow roasting pan. Add the hot broth to the pan; place the roasting pan in the oven. Lower the oven temperature to 350°F and roast for 45 minutes.
Carefully take the roasting pan out of the oven. Turn the duck breast-side up and replace onto rack. Dot the breast with half of the butter cubes and return to the oven. Roast for an additional 45 minutes to an hour (basting with the pan juices once and turning the roasting pan), or until you can until you can easily wiggle the legs in their sockets and the internal temperature of the thickest part of the drumstick reads 165°F. Remove the duck from the oven and place onto a cutting board; allow to rest for at least 15 minutes.
While the duck rests, prepare the sauce. Pour the vinegar into a saucepan over low heat with the peppercorns, chervil, and tarragon. Simmer until the vinegar has reduced by half. Strain into a bowl and allow to cool. Mix together the egg yolks, tomato paste, and cream to a heatproof bowl or double boiler. Season with 1/8 tsp. each salt and pepper. Set over barely simmering water; gradually whisk in the remaining butter. Remove sauce from heat and mix in the reduced vinegar. Check for seasoning.
Carve the duck and set onto a serving platter: make it pretty, garnishing with any remaining herb sprigs. Serve with sauce spooned over the slices of duck. Enjoy!