Steep the spices. In a medium saucepan, combine the milk, cream, vanilla paste or beans, cinnamon sticks, cinnamon, cloves, anise and half of the ground nutmeg. Bring to a gentle simmer, remove from the heat, and allow to steep for 30 minutes.
Temper the eggs. After 30 minutes, warm the milk mixture back up over medium heat. In a separate bowl, whisk together egg yolks and sugar until thick and pale yellow in color. Ladle a small amount of the warm milk into the egg yolks and sugar while whisking constantly. Repeat 3-4 times until the egg mixture is warm. The goal is to temper the eggs so that they don't scramble when they're added to the remaining milk.
Gently cook the eggnog. Whisk the egg mixture into the remaining milk while whisking constantly. Cook for 4-5 minutes over medium heat while whisking constantly until the eggnog has barely thickened.
Add the alcohol. Remove from the heat, whisk in the brandy, rum and remaining nutmeg.
Strain and chill. Strain through a fine mesh strainer into a heat proof container and transfer to the fridge until cold. The eggnog gets better with age, so it's best served the next day.
Make the whipped cream. Whisk the cream with powdered sugar and vanilla until thick. Top the eggnog with whipped cream and more freshly grated nutmeg, then serve.