One day ahead, remove the giblets from the chicken's cavity (save for a stock if you like -- but don't use 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. Generously and completely coat the chicken with the yogurt, rubbing it inside the cavity and under the skin. Set the chicken on a plate and cover with plastic, patting it down so that it clings, or seal the chicken in a plastic bag. Refrigerate overnight.
Heat the oven to 450°F. Sprinkle the outside and the cavity of the bird with the salt and pepper. Stuff a few mushrooms into the cavity. 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. Scatter the rest of the mushrooms in the roasting pan. Roast for 15 to 20 minutes, reduce the heat to 375°F, and continue to roast for about 1 more hour for a total of about 1-1/4 hours 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. With a slotted spoon, remove the mushrooms and keep them warm.
Make the sauce from the pan drippings (see photos). After adding the parsley, return the mushrooms to the pan, cook for a few seconds to warm them, and then taste and adjust the seasonings. Carve the chicken and serve the meat drizzled with some mushroom sauce.
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.