To a large bowl, prepare an ice bath by adding a heaping handful of ice cubes to a large bowl and topping it off with a few splashes of water. Set a slightly smaller bowl inside the larger bowl and place a sieve or strainer inside. Set the whole ice bath contraption aside.
Add the vanilla sugar, whole milk and brown sugar to a medium saucepan. Turn the heat to medium and stir until the sugar has dissolved and the milk is hot to the touch. Whisking the entire time, add about 1/4 cup of warm milk to the beaten egg yolks. Return the egg yolk and milk mixture back to the medium saucepan and place over medium low heat. Cook the mixture, stirring constantly, until the thermometer reads 170 to 175 degrees F and the custard appears thick and coats the back of a spoon.
Pour the custard through the sieve into the bowl. Stir in the heavy cream until completely incorporated. Next, add the whiskey, stirring until completely combined. Keep mixing until the mixture is room temperature. Place plastic wrap on the surface of the custard, which will prevent the surface from creating a skin, and transfer to the fridge for 4 to 5 hours, until very cold.
When the custard is cold, churn the mixture into the bowl of your ice cream maker, according to the maker's instructions.
Transfer the ice cream to a quart container and freeze until the ice cream is firm, about 4 to 8 hours.