Place the cubed bread in a large bowl. If your bread isn't already stale, you can lightly toast it in the oven at 300°F (150°C) for about 10 minutes to dry it out a bit.

In a separate bowl, whisk together the milk, heavy cream, eggs, sugar, cocoa powder, vanilla extract, and salt until well combined. Make sure there are no lumps of cocoa powder.

Pour the custard mixture over the cubed bread, making sure all the bread is evenly coated. Gently press down on the bread to submerge it in the custard. Let it sit for at least 30 minutes, or up to an hour, to allow the bread to soak up the liquid.

Gently fold in about half of the chopped bittersweet chocolate into the bread mixture.

Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish with butter or cooking spray.

Pour the bread pudding mixture into the prepared baking dish. Sprinkle the remaining chopped chocolate evenly over the top of the bread pudding. Dot the top with the small pieces of butter.

Bake for 45-50 minutes, or until the bread pudding is set around the edges but still slightly soft in the center. A knife inserted into the center should come out with some melted chocolate but not completely wet batter. The top should be golden brown and slightly crusty.

Let the Chocolate Lava Bread Pudding cool for about 15 minutes before serving.