Preheat the oven to 350 degrees F. Grease a 9-by-13-inch baking dish.
Microwave the heavy cream and milk in a medium microwave-safe bowl for 3 to 4 minutes, or until warmed. Whisk in the brown sugar, vanilla, salt and egg yolks.
Arrange half of the croissant pieces in the bottom of the prepared baking dish. Pour half of the heavy cream mixture over the croissants. Scatter two-thirds of the chocolate pieces over top and then dollop randomly with the marshmallow creme.
Layer the rest of the croissant pieces over the marshmallow creme, followed by the rest of the chocolate and then the rest of the heavy cream mixture. Press down lightly with your hands to make sure everything is submerged. Let sit for 10 minutes to allow the liquid to soak in.
Crush the graham crackers coarsely by hand while still in their sleeve and transfer to a medium mixing bowl. Rub the butter, granulated sugar and salt into the crumbs with your fingertips until combined. Scatter over the top of the bread pudding.
Bake the bread pudding until oooey, gooey and golden brown, 35 to 40 minutes. Spoon the melted ice cream "anglaise" over top.