After preparing Roast Chicken, remove rack from roasting pan, leaving necks in pan; place pan on stove (it may need to be set across two burners) over medium-high heat. Cook, stirring occasionally, until necks and chicken bits remaining in pan are deep brown, 3 to 4 minutes; spoon off and discard all but 1/4 cup of the fat.
Add 1 cup dry white wine, and boil until reduced by half, scraping up browned bits with a wooden spoon, 4 to 6 minutes. Carefully pour contents of pan through a fine-mesh sieve into a small saucepan; add any juices that have accumulated on platter from resting chickens.
Remove pan from heat; add 1 tablespoon cold butter, and swirl pan just until butter has melted and sauce has thickened. Season with coarse salt and ground pepper; serve with roast chickens. (If necessary, reheat sauce but do not boil.)