In a medium saucepan, combine 1 cup of cream with milk, sugar, and salt. Warm over medium-high, stirring occassionally, until sugar is dissolved and small bubbles begin to form around the edge of the pan (3-4 minutes).
Fill a large bowl with several inches of ice water. Set a smaller 2-quart metal bowl in the ice water. Pour 1 cup cream into inner bowl and set a fine strainer on top.
Whisk the egg yolks in another bowl and pour in half of the warm cream mixture, whisking constantly to prevent curdling.
Pour the egg mixture back into the saucepan and cook over low, stirring constantly and scraping the bottom with a silicone spatula. Cook until custard thickens slightly and coats spatula, about 4-8 minutes. Do not let the mixture overheat or boil.
Strain custard into cold cream in the ice bath. (Don't worry about curdled bits as they will be strained out.) Stir custard over the ice bath and cool to about 70°F.
Stir in peach puree and mascarpone, and chill for at least 4 hours.
Meanwhile, make the pie crust by combining flour, salt, and cold butter until pea-sized crumbs are formed, then slowly add ice water as you bring the dough together. Form into a disc, wrap in plastic, and chill for 1 hour.
Preheat oven to 350°F. After chilling dough, roll out flat and cut into small pieces. Place pieces on a baking sheet lined with parchment or a silicone mat. Sprinkle on cinnamon sugar and bake for 15 minutes, or until golden brown. Let cool completely.
Once ice cream mixture has chilled, churn according to your ice cream maker's instructions. Transfer to a freezer-safe container, layering in pie crust pieces as you fill the container. Enjoy!