In a blender or food processor combine peaches, cream, brown sugar, and corn syrup. Blend on high until all ingredients are very well combined, about 30 seconds.
Pour through a strainer into a heavy saucepan. Turn heat on medium high and bring base to a simmer, stirring frequently. Let simmer for 2 minutes, or until base becomes slightly syrupy, then remove from heat and transfer to an airtight container. Stir in salt to taste, ¼ teaspoon at a time, then add bourbon. Cover and chill overnight.
The next day, churn in ice cream maker according to manufacturer's instructions. Transfer to container and chill in freezer for 3 to 4 hours before serving.
