Step 1In a small bowl, whisk together the goat cheese and corn syrup until combined and smooth. Set aside.
Step 2In a small saucepan, bring the cream and milk to a boil over high heat. Remove from the heat. While the cream mixture is coming to a boil, whisk together the egg yolks and sugar in a mixing bowl.
Step 3Whisk one-fourth of the hot cream mixture into the eggs to temper them. Whisk in another quarter of the cream mixture, and then add the egg mixture to the cream in the saucepan. Continue to cook over low heat, stirring constantly, until the cream mixture thickens enough to coat the back of a spoon. Be careful not to overcook, or to cook at too high a heat, or the eggs will scramble. Immediately remove from the heat and strain, using a fine-mesh strainer, into a bowl set over a larger bowl of ice water.
Step 4Add the goat cheese mixture to the bowl and stir to combine, allowing the entire mixture to cool.
Step 5Freeze the goat cheese base in an ice cream machine according to the manufacturer's instructions. This will keep for 1 week frozen.