1. In a small saucepan, combine sugar and water. Bring to a boil.
2. Cook and stir over medium heat until sugar is dissolved. Increase heat to medium-high. Cook without stirring until mixture turns an amber color and a candy thermometer reads 300° (hard-crack stage).
3. Remove from the heat; gradually stir in milk.
4. In a small bowl, whisk the eggs. Whisk a small amount of hot milk mixture into eggs; return all to the pan, stirring constantly. Cook and stir over medium heat until mixture is thickened and coats the back of a spoon.
5. Pour in the Bailey's
6. Pour into a large bowl; stir in vanilla and nutmeg. Place bowl in an ice-water bath, stirring frequently until cooled. Refrigerate until chilled.
7. Before serving, whip cream until soft peaks form; fold into eggnog.
8. Top servings with grated nutmeg if desired