Preheat the oven to 250 degrees F. Spread the bread on a baking sheet and bake until crisp, about 30 minutes; let cool. Meanwhile, butter a 9-by-13-inch baking dish; set aside.
Combine the milk, sugar and salt in a medium saucepan over medium heat, stirring occasionally to dissolve the sugar; remove from the heat and let cool slightly. Whisk the eggs, egg yolks and vanilla in a large bowl. Pour the warm milk mixture into the eggs, whisking constantly.
Toss the bread with the apples and chocolate chips in a large bowl, then spread in the prepared baking dish. Pour the custard over the bread mixture, then gently press the bread down into the custard. Dot with the 2 tablespoons butter. Cover with foil and set aside 30 minutes.
Increase the oven temperature to 350 degrees F. Bake the bread pudding, covered, until a knife inserted into the center comes out clean, about 45 minutes. Uncover and continue baking until browned, about 15 more minutes. Let cool slightly; dust with confectioners' sugar and serve with whipped cream.