Melt the white chocolate in a heatproof bowl over simmering water, stirring until melted. Set aside and keep warm.
In a heavy-bottomed saucepan, heat the half-and-half, cream, vanilla seeds and pod, orange zest, spices, and salt over low heat until it comes to a boil. Stir occasionally to prevent scorching. Remove from the heat, cover, and steep for 20 minutes.
In the bowl of a stand mixer fitted with the whip attachment, whip the eggs and sugar on high speed until thick and ribbony, 3 to 4 minutes.
Strain the spices from the cream, return the cream to the pan, and reheat to a simmer. Lower the speed of the mixer to low. Slowly ladle some of the hot cream into the eggs, warming them up. Add them back to the pot of cream.
Attach an instant-read thermometer to the pot and cook the cream over low heat, stirring with a rubber spatula, until the cream reaches 170 degrees F.
Remove the saucepan from the heat; pour the mixture through a fine mesh strainer. This will remove any pieces of cooked egg and keep the eggnog smooth.
Whisk the hot strained eggnog into the bowl of white chocolate. Stir in the bourbon and rum. Pour into 4-ounce cups. Garnish with whipped cream, grated nutmeg, and homemade marshmallows. Best if consumed while hot, creamy, and delicious.