In a large bowl, beat 6 eggs. Gradually add milk and sugar into bowl while whisking. Simmer egg mixture on lowest heat possible until it thickens just slightly. Add in vanilla extract and nutmeg. Cover and refrigerate until chilled.
To rim glasses, spread pumpkin spice and sugar on a plate and dip glass rims into eggnog, then roll in cinnamon sugar mixture. Pour spiced rum into eggnog once chilled. Stir and pour into rimmed glasses. Top with an additional sprinkle of fresh nutmeg and star anise. Enjoy!