In a large bowl, whisk together the condensed milk and evaporated milk and the egg yolks. Stir until the mixture is well combined.Sieve, then discard solids. Add cinnamon sticks and nutmeg.
2. Cooking ingredients
Boil in a medium pot in a bain-marie (hot water bath) over medium-low heat for 20 minutes, lower heat and simmer for 20 more minutes. Stir often with a wooden spoon to prevent it from sticking to the bottom.
3. Cooling
Add the rum and remove it from the heat. Stir constantly but slowly until it cools down to room temperature.Remove the cinnamon sticks.
4. Chilling and serving
Chill, then ladle into a bottle for storage, or to serve immediately.
Video
Notes
Don't worry if it's not as thick as you're used to when you finish cooking, it will get thicker when chilled.