Heat the oven to 450°F. Remove the giblets from the chicken's cavity (save for a stock if you like -- but don't include the liver, which would make the stock bitter). Pull any loose fat from around the opening. Rinse the bird inside and out and pat dry. Rub the chicken all over with the softened butter, gently pushing the butter under the breast skin. Sprinkle the outside and the cavity with the salt and pepper and stuff the herb sprigs inside.
Put the chicken, breast side up, on a V-shaped rack (or a flat rack) and set the rack in a roasting pan just larger than the rack. Roast for 15 to 20 minutes, reduce the heat to 375°F, and continue roasting for an additional 45 minutes for a total of about 1 hour for a 3-lb. chicken. (For larger birds, add another 10 minutes for each additional pound.) The chicken is done when the leg wiggles freely in its joint and when the juices run clear from the thigh when you prick it and from the cavity when you tilt the bird. A thermometer inserted into the lower meaty part of the thigh should register 170°F. Set the chicken on a warm platter, propping up the hindquarters with an inverted saucer, and tent with foil to keep it warm while you make the sauce. Remove the rack from the pan.
Make the sauce from the pan drippings: Tilt the pan and spoon off as much fat as possible. (Be sure to reserve some of the fat for the vinaigrette.) Set the pan over high heat to caramelize all the juices, but be careful not to let them burn. Deglaze the pan with the cognac or brandy, scraping up all the drippings. Boil until the liquid is just a syrupy glaze, add about 1-1/2 cups of the broth, and boil it down to a sputtering, bubbling glaze. Repeat with another 1-1/2 to 2 cups broth, boiling that down until it's reduced to about 2/3 cup sauce. Add the herbs and cream (if using); taste and adjust the seasonings.
Make the salad and serve: Whisk the shallot, vinegar, and mustard in a small bowl. Whisk in 3 Tbs. of the reserved warm chicken fat, and add salt and pepper to taste. Toss with the greens and serve immediately with the carved chicken, drizzled with some sauce.