Preheat your oven at 350 degrees.
For the bread pudding, cut the croissants into 1 inch pieces and place in a large bowl.
In a medium saucepan over low heat, melt brown sugar, milk, butter, cinnamon stick, vanilla and dark rum. Stir constantly until sugar is dissolved.
In a small bowl, whisk your eggs. Slowly add into the eggs some of the warm milk mixture, couple tablespoons at a time while whisking the eggs. This ensures you don't end up with scrambled eggs. Whisk to combine and add the egg mixture into the remaining custard.
Carefully pour your custard over the croissants and fold the bread to ensure all of the bread is fully coated.
Cover your custard bread mixture and allow it to rest for 10 minutes. This ensures the croissants fully soaks in the custard.
Pour half of your bread into a greased 9x9 casserole dish and sprinkle with half of your chocolate chips. Top with the remaining bread pudding and remaining chocolate chips.
Cover with tented aluminum foil and bake for 30 minutes. Uncover the bread pudding and bake for an additional 15 minutes.
To make your rum sauce, place the heavy cream, white sugar, and butter in a medium saucepan over low heat. Be sure not to let the mixture boil or it will crystallize. When sugar has dissolved, add in the rum. Pour the warm sauce over each slice of bread pudding before serving.