Separate the eggs and beat the egg yolks on a double boiler for a couple of minutes.
Add the powdered sugar and beat until smooth.
Add the evaporated milk and the heavy whipping cream and beat on the double boiler until the mixture thickens to a creamy consistency. This step needs some patience as it will take about 5 to 10 minutes. Be careful that the mixture does not boil.
Add the brown rum and stir for an additional about 3 to 4 minutes until it is thick and creamy.
Remove the mixture from the heat and pour into clean bottles.
Leave 1 inch of the bottle empty. The liquid will thicken over time and it can be difficult to pour it easily. Just add a shot of liquid heavy whipping cream or rum and shake well.