Lightly butter a round baking dish (dia 9 1/2-inch). Tear bread into large pieces; scatter evenly in prepared baking dish. Set aside.
In a medium bowl, whisk together eggs, sugar and vanilla; set aside.
In a medium saucepan, combine milk, chocolate chips and butter. Place over medium-low heat until chocolate is melted, about 5 minutes, stirring occasionally.
Whisk egg mixture in warm milk mixture until combined.
Preheat oven to 350 degrees F. Pour mixture evenly over bread and push bread down into liquid.
Bake until pudding has puffed and is firm (a toothpick comes out clean), about 25-30 minutes. Cool at least 10 minutes. Dust with confectioners' sugar just before serving.