Pour the Half & Half into a heavy-based saucepan and add the sugar. Place on a medium heat and whisk until the sugar dissolves.
Whisk egg yolks in a bowl then gradually pour on the hot milk. Rinse out the saucepan and return milk mixture to the saucepan. Cook at a gentle simmer until the eggnog is thick and creamy, stirring continuously. Do not allow it to boil or it will curdle.
Strain eggnog into a jug and stir in the cream. Leave to cool completely before pouring into glasses and grating over fresh nutmeg.