Preheat oven to 350 degrees. Spray 4 medium-sized ramekins with non-stick spray. Tear each croissants into bite sized pieces and fill each ramekin. Place the ramekins on a baking sheet covered with parchment paper or foil to make clean-up easy.
In a sauce pan, combine sugar and water and set to medium-high heat. Caramelize the sugar and water mixture by letting it bubble away, without stirring (it is very important that you resist the urge to stir the mixture), until it turns a deep amber color, about 7-10 minutes. Once it turns to the desired color, reduce the temperature to low. (if you double this recipe, it will take longer).
In a two cup measuring cup, combine the heavy cream and whole milk. When sugar has caramelized, add the cream and milk mixtures slowly the caramelized sugar, whisking vigorously. The mixture will bubbly and let off a lot of steam. Be careful not to get a steam burn! Turn the heat off and add the rum. Keep whisking for about an minute. Slowly add the beaten eggs, whisking the whole time to prevent scrambling. Sauce will thicken slightly.
Pour the custard over the croissant, dividing it evenly between the four ramekins. Let the custard soak into the croissant for 5-10 minutes, spooning more custard until it is completely divided between the ramekins.
Bake uncovered for 20-25 minutes until bubbling and the tops have turned golden brown. Let cool for 5 minutes and garnish with powdered sugar. Serve with oven bacon. Enjoy!