In a large saucepan, whisk together sugar and cornstarch until combine. Pour in cream, milk and corn syrup and whisk until well blended. Cook mixture over medium heat (sometimes I even cook it over medium high to speed it up a bit), stirring constantly until mixture comes just to a gentle boil.
Once mixture reaches a gentle boil, reduce heat and allow mixture to gently bubble, stirring constantly, for 30 seconds. Strain mixture through a fine mesh sieve into a large bowl. Cover mixture with saran wrap or wax paper, pressing directly against the surface of the ice cream base to prevent a skin from forming.
Refrigerate mixture until fully chilled, then transfer to freezer and freeze 1 hour - 1 1/2 hours (I've found this really helps the ice cream structure when freezing post ice cream maker processing, it basically gives it a head start). Transfer extra chilled ice cream mixture to an ice cream maker and freeze according to manufacturers directions.
Transfer ice cream to an airtight container and freeze until nearly firm, or freeze until firm and soften in microwave about 5-10 seconds until slightly softened. Mix in desired "mix-ins" (if you wanted to prepare just as Cold Stone does, you could freeze a marble slab then use two large spoons to fold in mix-ins using chilled marble slab, or alternately you could add the mix-ins in during the last 5 minutes of processing in ice cream maker).