In a large bowl, whisk the egg yolks, cream, sugar, and salt until thoroughly combined.

In a medium saucepan over medium-high heat, bring the milk to a gentle boil.

Remove the milk from the heat and, whisking constantly, slowly pour it into the yolk mixture to temper. Return the milk-yolk mixture to the saucepan and place over medium-low heat. Cook gently, whisking constantly, until the mixture is slightly thickened and reaches between 160°F-165°F on an instant-read thermometer, 2 to 3 minutes; do not let boil.

Set a fine mesh strainer over a large clean bowl. Pour the eggnog through the strainer into the bowl. Whisk in the rum, nutmeg, and cinnamon. Let the eggnog come to room temperature, then cover with plastic wrap and chill in the refrigerator until cold, at least 3 hours and up to 3 days.