Combine milk, cream, vanilla bean cut open and seeds scraped into milk, nutmeg and cinnamon sticks on a pan on the stove. Heat till the edges just begin to bubble, stirring on a regular basis.
Once the edges are bubbling, remove from heat.
Combine egg yolks with sugar and vanilla extract. Beat until the eggs are lighter in color and sugar is dissolved.
Slowly temper the eggs with the warm milk by combining ½ cup of milk at a time with a hand mixer. Once the eggs are tempered, continue to combine the eggs and milk completely. refrigerate until ready to serve.
When ready to serve, beat the egg whites until peaks form. Cut into the eggnog and pour the rum into the mixture. Serve immediately.
Save leftovers for up to three days.