Preheat oven to 325 degrees F. Grease a 2-quart square baking dish; set aside. Place bread pieces on a shallow baking sheet. Bake for 7 to 8 minutes or until dry and crisp; cool.
In medium bowl lightly beat eggs. Stir in sweetened condensed milk, the 3/4 cup milk, the vanilla, and nutmeg; set aside.
Place bread pieces in prepared baking dish. Sprinkle with 1/2 cup each of the marshmallows and chocolate pieces. Evenly pour milk mixture over all. Let stand for 5 minutes. Sprinkle with crushed graham crackers. Bake, uncovered, for 35 minutes. Sprinkle with 1/4 cup of the remaining marshmallows. Bake about 5 minutes more or until a knife inserted near center comes out clean. Cool for 20 to 30 minutes.
Meanwhile, for chocolate drizzle, in a small saucepan combine the remaining 1/4 cup marshmallows, the remaining 1/4 cup chocolate pieces, and the 2 tablespoons milk. Cook over low heat until melted and smooth, whisking constantly.
To serve, spoon bread pudding into glasses or bowls. Top with chocolate drizzle.