Whisk the eggs in a large bowl. Whisk in the half-and-half, eggnog, granulated sugar, brown sugar, vanilla, 1 teaspoon nutmeg, the cinnamon and salt. Arrange the challah slices in 2 lengthwise rows in a 9-by-13-inch baking dish, shingling the slices. Pour the egg mixture all over the challah and gently press down. Cover with plastic wrap and refrigerate overnight.
Preheat the oven to 350 degrees F. Combine the turbinado sugar and remaining 1/2 teaspoon nutmeg in a small bowl. Uncover the challah and sprinkle with the sugar mixture. Bake until browned and puffed, 35 to 40 minutes. Let sit 10 minutes. Dust with confectioners' sugar. Serve with whipped cream and/or syrup.