Separate the eggs, reserving the whites for another use. Beat yolks with half of the sugar until thick and lemon-colored. Gradually add rum while beating.

In a saucepan over medium heat, combine milk, pumpkin puree, vanilla extract, and cinnamon. Bring to a simmer but do not let it boil! Slowly pour into the egg mixture in a thin stream while constantly whisking – this tempers the eggs, so they won’t scramble when added back to the hot liquid mixture.

Continue cooking over low heat just until very warm (do not allow it to come near boiling). Pour into cups or mugs through a fine strainer if lumps remain after passing through cheesecloth (optional). Chill thoroughly.

Whip the egg whites and fold them into the mixture slowly.