Add cream, milk, cinnamon, nutmeg and a splash of vanilla to a saucepan on medium heat. For an incredibly rich ice cream, you can use all heavy cream. Bring the liquid to a gentle simmer.
While the cream is warming up, whisk egg yolks and sugar together in a bowl. Make sure they're well combined.
When the cream is just starting to simmer (don't boil it), slowly temper it into the yolks while whisking.
Pour the mixture back into the saucepan and turn the heat down to medium low. Stir in a figure 8 motion with a wood spoon for several minutes until the mixture coats the back of the spoon. Remove from the heat. Continue to stir over an ice bath until cool. Stir in rum.
Chill in the refrigerator until cold.
Make ice cream according to the manufacturer's instructions.
Serve with fresh grated nutmeg and cinnamon on top.