In a medium saucepan, combine whole milk, heavy cream, cinnamon sticks, ground cinnamon, ground cloves, star anise, and vanilla bean paste. Heat over medium-low for about 15 minutes until it just begins to simmer, then let steep for 30 minutes.

Whisk egg yolks and granulated sugar in a large bowl until thick and pale. Slowly drizzle in the warm milk mixture, incorporating gently.

Pour the tempered egg mixture back into the saucepan with the spiced milk. Cook over medium heat, whisking constantly for 4-5 minutes until thickened and reaches at least 160°F.

Remove from heat and whisk in brandy and dark rum. Stir in more freshly grated nutmeg.

Strain through a fine mesh sieve into a clean container, discarding solids. Refrigerate until cold, preferably overnight.

Just before serving, whip heavy cream with powdered sugar and vanilla until stiff peaks form. Garnish eggnog with whipped cream and grated nutmeg.