Preheat your oven to 350°F (177°C). Begin by combining the melted butter with the milk and, if desired, the espresso powder. If the butter solidifies upon mixing with the milk, gently warm the mixture in the microwave in 15-second intervals, stirring after each interval, until the butter fully incorporates. Set this aside.

Grease a baking dish lightly with a small amount of butter to prevent sticking. Spread the chocolate cake mix evenly across the bottom of the dish, ensuring a level layer. Sprinkle the instant chocolate pudding mix over the cake mix, distributing it uniformly to create a consistent base for the wet ingredients.

Carefully pour the butter and milk mixture over the dry layers. Using a spoon or spatula, gently combine the wet and dry components until no large pockets of dry mix remain. Be cautious not to overmix; the texture should remain slightly rustic.

Scatter the chocolate chips evenly over the surface of the cake batter.

Place the baking dish in the preheated oven and bake for 35 to 45 minutes, or until the top is set and slightly crisp. Allow the cake to cool for 10 to 15 minutes before serving.

For a decadent treat, scoop portions into bowls and top with a dollop of ice cream, if desired. Enjoy the rich, chocolatey indulgence!