In a glass measuring cup, combine the eggnog, milk, and heavy cream. Set aside.
Add sugar, cornstarch, salt, cinnamon, and nutmeg to a medium saucepan and whisk together.
Add egg yolks and whisk until combined and smooth.
Slowly pour the eggnog mixture into the egg mixture while whisking constantly until combined.
Place saucepan on the stove and heat on medium heat. Cook, stirring constantly until the mixture is thickened and begins to boil. Mixture should coat the back of a spoon.
Remove from heat and add rum extract and stir.
Place pudding in a bowl.
Cover bowl with plastic wrap, placing the plastic directly on top of the pudding so it doesn’t form a skin while cooling. Chill in the refrigerator for 4 hours or preferably overnight.