Whisk egg yolks and sugar in a large bowl, until smooth. Combine milk, cinnamon, and cloves in a large saucepan and heat slowly until mixture just reaches a boil. In a thin stream, whisk the hot milk into the yolks and sugar, whisking constantly. Return mixture to pan and cook over low heat, stirring frequently with a wooden spoon, until mixture coats the back of the spoon (about 12 minutes; do not let mixture boil). When thick, pour into a large bowl and let cool. Stir in the half-and-half and rum, if using. Chill for 3 hours or overnight. Sprinkle each serving with grated nutmeg and serve with a cinnamon stick.