Grease a 9-by-13-inch baking dish with butter or cooking spray.
In a large bowl, whisk the half-and-half, milk, granulated sugar, vanilla, cinnamon, salt, hot chocolate mix, whole eggs and egg yolks. Stir in the bread cubes until evenly coated. Stir in the chocolate chips and marshmallows. Transfer the mixture to the prepared baking dish. Cover and refrigerate for at least 1 hour and up to overnight.
Preheat the oven to 350 degrees F.
Bake until golden brown, 55 minutes to 1 hour. Let stand 10 minutes before cutting. Serve dusted with confectioners' sugar and a dollop of whipped cream.