Make the dough: Pour ½ cup of water into a measuring cup filled with ice cubes. Set aside. Place the cubes of butter on a parchment-lined baking sheet and place it in the freezer for about 15 minutes to quickly chill.

In a large bowl, whisk together the flour, sugar, and salt. Add the chilled butter to the flour mixture and cut the butter into the flour until there are no visible bits of butter that are larger than a pea.

Pour ¼ cup of the ice water into the flour and butter mixture. Using your hands, gently work the water into the flour mixture until the dough comes together.

Lightly flour your work surface and set the dough on top. Gently knead the dough into a ball. Wrap the dough well in plastic wrap and refrigerate for at least 1 hour.

While the dough chills, fill a large bowl or a large baking dish with ice cubes to chill your work area.

Remove the chilled dough from the refrigerator and pat the countertop dry. Lightly flour the surface and roll out the pie dough to about 12 inches in diameter.

Transfer the dough to a 9-inch pie pan and crimp the edges. Place the pie shell in the refrigerator to chill for 10 minutes.

Make the Salted Caramel Sauce: In a small saucepan, warm the heavy cream over medium-high heat until it is steaming. Set aside.

In a medium saucepan over medium-high heat, add the sugar and allow it to caramelize while constantly stirring until it turns deep amber.

Add the butter to the caramelized sugar and whisk until the butter melts. Remove from heat and whisk in the warmed heavy cream, vanilla, and salt.

Make the pie: Preheat the oven to 350°F (175°C). In a large bowl, whisk together the melted butter, egg, granulated sugar, brown sugar, salt, vanilla, cinnamon, and nutmeg until smooth.

Stir in the flour and oats, then fold in the peaches until well incorporated. Pour the filling into the chilled pie shell.

Bake until a cake tester or toothpick inserted in the center comes out dry, about 1 hour 10 minutes. Allow to cool for 15 minutes before serving with salted caramel sauce.