Start up your grill, prepare it for indirect heat, have it running at 130° C / 265° F.
Put the egg yolks in a bowl and add the sugar a few tablespoons at a time while whisking. Keep whisking until the mix is light and fluffy.
Pour the cream and milk into a disposable aluminum pan together with the cloves and cinnamon. Place the pan on the grill on the cooler side and add a few wood chunks to the glowing embers for smoke flavor. Now put the lid back on.
Leave the pan for 10 minutes, then open the grill and whisk a few times to blend things together, and smoke for another 10 minutes. You want the milk/cream mix to get warm, but it must not boil.
Mix milk/cream and eggs
Now it's time to mix the contents of the bowl and pan. It's important to go slow here to avoid lumps.
Carefully pour 1/3 cup of the milk/cream mix at at time into the egg mix while constantly whisking. It's important to not add all of the milk/cream mix too fast, since the eggs are cold and the milk is warm. Keep going until everything's in one bowl.
Now put the mix back into the grill/smoker for another 15 minutes. Stir a few times during that time.
Remove the bowl or pan with the egg nog and run it through a strainer to get rid of the cloves, cinnamon and any lumps.
Leave the eggnog to cool a bit before spiking it with bourbon or rum. Serve in small glasses or mugs.