Using a food processor or blender, puree the peaches, corn syrup, schnapps and salt. Pour into a 9-inch square metal baking pan and freeze for 4 hours. (Or freeze in an ice cream maker according to the manufacturer's instructions.)
In a small bowl, using a handheld electric mixer, beat the mascarpone and sugar until smooth. Gradually mix in the cream and beat until soft peaks form, about 4 minutes.
Using a fork, break apart and shave the frozen peach mixture into small ice crystals (or process in a food processor). Serve in small parfait glasses with dollops of the mascarpone cream.