Reduce the 1½ liters of root beer down to 2 cups in a medium saucepan over medium heat. This should take about an hour, so pull up a chair and a good book.
In a medium saucepan over medium heat, mix together the sugar, milk, and light corn syrup. Heat, stirring often, until right before it boils. Remove from heat.
Add the reduced 2 cups of root beer, 1 cup of unreduced root beer, and 1 teaspoon vanilla extract to the milk mixture and stir to combine.
Cover and chill in the refrigerator for about 8 hours.
Follow the directions on your ice cream maker to mix the batter into ice cream, until it reaches the desired consistency. This is the conversion process.
Freeze for another 2 to 4 hours while the ice cream hardens and ripens. Note: if you taste the ice cream before you ripen it in the freezer, it will taste very sweet. This sweetness subdues after freezing.