In the bowl of a stand mixer beat together the egg yolks and sugar until the yolks lighten in color and the sugar is completely dissolved. Set aside.

In a medium saucepan, over medium heat, combine the milk and heavy cream and bring just to a simmer, stirring occasionally. Decrease the heat to low and temper in the egg mixture. Cook until the mixture just begins to thicken, approximately 5 minutes. Remove from the heat, stir in the nutmeg, bourbon and rum. Pour into a medium mixing bowl and set in the refrigerator. Chill the mixture in the refrigerator until it reaches a temperature of 40 degrees F, stirring occasionally. Once chilled, process in an ice cream maker according to the manufacturers' instructions. Place in an airtight container and put in freezer for 2 hours before serving