Combine eggs and sugar in a medium bowl and whisk until thoroughly combined. Transfer to a saucepan and stir in whole milk, vanilla extract, and ground nutmeg.
In a separate bowl, stir evaporated milk and half and half until combined. Set aside.
Heat egg mixture over medium-low heat while stirring constantly to prevent the milk from scorching. When mixture reaches 160 degrees on a candy thermometer, remove from heat and slowly whisk in evaporated milk mixture.
Cool slightly before tasting. Add more sugar or nutmeg, if desired, before transferring to an airtight container. Refrigerate overnight or until thoroughly chilled. Serve in mugs and garnish with whipped cream, cinnamon sticks, and/or a dash of nutmeg, if desired. Enjoy!