Combine sugar, honey, and water in a small pot. Stir over medium heat until sugar dissolves. Increase heat and boil for about three minutes. (Watch carefully so that mixture does not burn.) Meanwhile, beat egg white and salt in a mixing bowl until soft peaks form. With mixer running, gradually pour hot syrup into egg whites in a thin stream. Beat until meringue is thick and has tripled in volume, about 10–12 minutes. Remove bowl from the mixer and add nuts and dried cranberries to meringue; mix to distribute evenly.

Transfer nougat to a greased, eight inch square pan, spreading in an even layer. With damp hands, press nougat into an even layer. Let stand at room temperature, about two hours. Run a sharp knife under hot water, wipe dry, and cut nougat into small squares, reheating knife if necessary. Store airtight at room temperature.