Prepare the Egg Nog Base: In a medium saucepan, combine the heavy cream, whole milk, and sugar. Heat over medium until hot but not boiling, stirring occasionally. In a separate bowl, whisk the egg yolks until smooth. Slowly pour a small amount of the hot milk mixture into the egg yolks while whisking to temper the eggs. Gradually add the remaining hot mixture to the egg yolks. Return the mixture to the saucepan and cook over low heat, stirring constantly, until the custard thickens enough to coat the back of a spoon. Remove from heat and stir in cinnamon, nutmeg, and vanilla extract. Let the mixture cool to room temperature.
Chill the Mixture: Transfer the cooled egg nog base to the refrigerator and chill for at least 3-4 hours or overnight to ensure it’s thoroughly cold before freezing.
Freeze the Mixture: Pour the chilled mixture into the Ninja Creami pint container, secure the lid tightly, and freeze for at least 24 hours, ensuring the mixture is completely solid.
Process in the Ninja Creami: Once frozen, remove the pint from the freezer and insert it into the Ninja Creami ice cream maker. Select the "Ice Cream" setting and allow the machine to process the mixture for 2-3 minutes, or until it reaches a smooth, creamy texture. If needed, use the "Re-spin" function to achieve a firmer consistency.
Serve: Scoop and serve the ice cream immediately. You can enjoy it on its own or pair it with other holiday treats like pies or warm drinks.