To begin, separate 5 eggs. You will need the yolks for this recipe.
Place the yolks in a small dish and whisk them smooth.
Set the bowl near the stove as you will want it handy later on. (Store the whites in an airtight container in the fridge and make yourself an egg white omelette in the morning!)
In addition to the yolks, measure out the rum, butter, and salt.
Place them near the stove as well.
In a saucepan, combine the brown sugar and water. Bring it to a rolling boil and boil for 2 minutes.
Turn off the heat. In another saucepan, combine the corn starch and milk. Whisk them until smooth and then cook over medium heat, stirring continually until the mixture begins to boil. Let it boil for 1 minute and then turn off the heat.
Now for your eggs. While whisking quickly, slowly drizzle a couple ladles of the hot milk into the eggs to temper them and keep them from turning into scrambled eggs in your pudding.
Return all of the milk and egg mixture to the saucepan with the hot milk gravy. Pour in your brown sugar syrup.
Whisk this all together and over medium heat return it to a boil.
Boil 1 minute while stirring continually.
Add in the butter, rum, and salt and stir until completely combined.
Pour the pudding through a sieve to rid of any lumps that may have developed.
Spoon the pudding into serving dishes and chill for an hour. When you are ready to serve, drizzle a tablespoon of caramel sauce on top (such as my homemade one.)
Top with a dollop of whipped cream and some chocolate shavings.