Place Smith's milk, sugar, baking soda, cinnamon, clove and orange zest in a saucepan.
Watching carefully, bring to a simmer, lower heat, cover and simmer for 5 minutes. Do not walk away because you must adjust the heat after covering it, or it might boil over.
Remove from heat, still covered, and steep for 30 minutes.
Uncover milk mixture and strain out cinnamon sticks, clove and orange peel. Stir in nutmeg.
Allow to cool while separating eggs and placing yolks in the bowl of a mixer. Beat yolks until pale yellow and thick.
Ladle in warm milk mixture in a thin stream while beating on medium-high speed to prevent eggs from cooking.
When all milk has been added, return to saucepan and cook over medium-low heat, stirring constantly, until nog has thickened enough to coat the back of a spoon.
Remove from heat and stir in vanilla and rum.
Serve warm or, even better, chill overnight to allow flavors to blend before serving.