In a 4 quart saucepan, whisk 2 cups milk, heavy cream, corn syrup, sugar, and salt. Bring to a boil over medium heat. Watch closely and whisk often.
In a separate bowl, whisk together the cornstarch and reserved 2 tablespoons milk until smooth. Set by the saucepan.
As the mixture comes to a low boil, whisk to ensure all the sugar is dissolving. Allow the mixture to boil slowly for 2 minutes. Then remove from heat and whisk in the cornstarch mixture. Return to heat and whisk until the mixture is bubbling throughout.
Remove from heat and stir in the vanilla, orange extract, and orange zest. Let cool to room temperature, about 20 minutes. Then pour into an airtight container through a strainer to remove any lumps and any zest.
Chill at least 6 hours.
When the ice cream base has chilled, remove it from the refrigerator and pour it into the ice cream maker. Add the champagne on top of the ice cream base.
Follow the instructions with your maker as they may vary depending on the manufacturer. Insert the paddle and churn until thick. With a KitchenAid ice cream attachment, this takes about 25-30 minutes.
When the ice cream has churned, scoop it into an airtight freezer container. Freeze 4-6 hours before enjoying to ensure it is at a good scooping consistency.