Beat the eggs, then add the eggnog, melted butter, vanilla, and nutmeg, whisking to combine evenly. Add sugar and whisk until sugar is dissolved. Toss together the bread doughnut cubes and fresh cranberries. Generously butter a 9-inch baking dish. Arrange the doughnut bread cubes and cranberries tightly in a nine-inch baking dish. Pour liquid over the doughnuts. Press down lightly on the stale doughnuts to help them absorb the custard. Butter a piece of foil and place buttered side down over the dish. Allow it to rest in the refrigerator for at least an hour or overnight so the doughnuts can soak up the custard. Let the pan rest on the counter top while you preheat the oven to 325°F. Place a bread or cake pan full of boiling water on the lower shelf. Bake the bread pudding on the upper shelf for 55 to 70 minutes, removing the foil after the first 40 minutes, or until the bread pudding is puffy and the crust is golden brown all over the top. Remove the Cranberry Eggnog Doughnut Bread Pudding from the oven and allow it to cool and set up for 30 minutes before scooping and serving. If desired, dust with powdered sugar before serving.