Pour the water into a medium saucepan and begin to heat over medium heat.
Add the brown sugar, cinnamon stick, cloves, and nutmeg. Stir to combine, then let it warm until the sugar is completely dissolved.
Pour in the freshly squeezed lemon juice, then stir to allow the flavors to meld.
In a separate bowl, whisk the egg yolk until it is slightly frothy.
While whisking constantly, slowly drizzle the hot mixture into the egg yolk, ensuring the egg doesn't curdle, but thickens the drink nicely.
Pour everything back into the saucepan and continue to stir over low heat for a few minutes until it thickens slightly. Do not boil!
Finally, add the rum and stir thoroughly.
Strain the drink, then pour into a mug or heat-resistant glass. Serve hot, optionally garnished with a cinnamon stick.
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