Preheat oven to 325 degrees F (165 degrees C). Grease a 2-quart square baking dish. Spread hot dog bun pieces out onto a baking sheet.
Bake hot dog buns in the preheated oven until dry and crisp, 7 to 8 minutes. Cool completely.
Beat condensed milk, 3/4 cup milk, eggs, vanilla extract, and nutmeg together in a bowl.
Spread hot dog bun pieces out in the bottom of the prepared baking dish. Pour milk mixture over buns. Scatter 1 cup marshmallows and 3/4 cup chocolate chips over the milk mixture; let rest until mixture is slightly soaked into bread, about 5 minutes. Sprinkle graham cracker crumbs over the top.
Bake in the preheated oven until a knife inserted into the center of the bread pudding comes out clean, about 35 minutes.
Whisk 2 tablespoons milk, 2 tablespoons marshmallows, and 2 tablespoons chocolate chips together in a saucepan over medium heat until marshmallows and chocolate are melted and completely incorporated. Pour marshmallow mixture over bread pudding and cool, 20 to 30 minutes.
