Heat the oven to 450°F. Remove the packet of giblets from the cavity of the chicken (and save for use in a stock if you like -- but don't include the liver, which will make the stock bitter). Pull any loose fat from around the opening. Rinse the chicken inside and out, and pat dry with paper towels. Rub the outside of the chicken with about 1 Tbs. of the softened butter. Mix the remaining 2 Tbs. butter with the chopped lemon zest and herbs. Rub the butter on the inside of the cavity and under the breast skin (see photos). Sprinkle the inside and outside of the bird with the salt and pepper. Pierce the whole lemon with a sharp knife and put it in the cavity of the chicken. Brush the garlic halves liberally with the olive oil and reserve.
Slip your seasonings under the skin for full flavor and moist meat. Rub the chicken all over with softened butter, gently pushing the butter and other seasonings under the skin without tearing it.
Fill the cavity with flavor: Season the bird inside and out with salt and freshly ground black pepper, and stuff the cavity with herbs, lemon, mushrooms -- whatever will enhance the flavor of the meat and the sauce.
Lift the bird with a rack so the skin crisps all around. A V-shaped rack is best, set in a heavy roasting pan just larger than the rack, but a flat rack is better than nothing.
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. Cut the zested lemon in half and squeeze both halves over the chicken. Roast for 15 to 20 minutes, reduce the heat to 375°F, set the garlic halves in the pan near the chicken, and continue roasting for about 45 minutes more 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 (see photos). Carve the chicken and serve the meat drizzled with some sauce and with the roasted garlic on the side.
Good drippings are the foundation for a good sauce. Tilt the pan and spoon off as much fat as possible. Set the pan over high heat to caramelize all the juices, but be careful not to let them burn.
Wine provides backbone and stock gives body. Deglaze with the wine, cognac, or sherry, scraping up all the drippings. Boil until the liquid is just a syrupy glaze, add about 1-1/2 cups of the stock, and boil it down to a sputtering, bubbling glaze.
A second reduction adds layers of complex flavor. Repeat with another 1-1/2 to 2 cups stock, boiling that down until it's reduced to about 2/3 cup sauce. Add any herbs or cream, taste, and adjust the seasoning.