Peach Pie Ice cream

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INGREDIENTS:⠀

2 3/4 cups all-purpose flour⠀
1 tablespoon brown sugar⠀
1 1/2 teaspoons kosher salt⠀
18 tablespoons unsalted butter, cubed and chilled⠀
6 tablespoons ice water⠀
2 egg whites, beaten⠀
1 tablespoon water⠀
1/4 cup sanding sugar⠀
BOURBON CARAMEL:⠀
1/2 cup water⠀
1 1/4 cups sugar⠀
1/2 teaspoon kosher salt⠀
1 cup heavy cream⠀
1 1/2 teaspoons bourbon⠀
ICE CREAM:⠀
1 (1.75-quart) container old-fashioned vanilla ice cream, divided⠀
1 ripe but still firm peach, pitted and diced, divided⠀
1 batch bourbon caramel sauce⠀
PEACH COMPOTE:⠀
6 ripe peaches, peeled, pitted and roughly chopped⠀
1/4 cup sugar