Put milk and 1 cup of the cream into a heavy saucepan over medium heat. Sprinkle in cinnamon, nutmeg, cloves, and salt.
Heat mixture until it’s just about to come to a boil (but don’t let it actually start boiling), then turn heat to low, cover, and let the mixture sit for about 30 minutes so the spices can seep.
Pick out cloves and add in sugar. Stir to dissolve sugar.
Whisk egg yolks in a medium heat-proof bowl. Slowly pour about half the warm milk mixture into the bowl with the egg yolks, whisking the entire time (this method will help temper the egg yolks so they don’t start cooking). Now pour this mixture back into the saucepan with remaining milk.
Turn the heat back up to medium and stir with a wooden spoon until the mixture thickens up enough that it coats the back of the spoon.
While you’re waiting for your mixture to thicken (should take about 10-15 minutes), place a heat-proof bowl with the remaining 1 cup cream over a larger bowl filled with an ice bath. Strain the heated mixture into the cold cream, stirring constantly.
Place bowl in the fridge to continue chilling for at least 4 hours.
Once chilled, stir in vanilla and rum and process the mixture in your ice cream maker according to manufacturer’s instruction. Put ice cream it in airtight containers and freeze again, for at least 4 hours to harden ice cream.
Spread about a quart of eggnog ice cream into cooled gingersnap crust. Place back in the fridge for another hour and then slice and serve with whipped cream on top