2 sticks (1 cup) unsalted butter, at room temperature and cut into small pieces, plus more for greasing the baking sheet
3 cups all-purpose flour
2/3 cup confectioners' sugar
1/2 teaspoon kosher salt
3 pounds peaches (about 6 peaches), cut into 1/2-inch wedges
1 1/2 cups firmly packed light brown sugar
Juice of 1 lemon
3 tablespoons cornstarch
2 teaspoons pure vanilla extract
1 teaspoon ground cinnamon
1/4 teaspoon freshly grated nutmeg
3/4 cup all-purpose flour
1/2 cup sliced skin-on almonds
1/2 cup firmly packed light brown sugar
6 tablespoons unsalted butter, melted
1/4 teaspoon kosher salt
Special equipment: A rimmed 10-by-15-inch baking sheet
Adjust a rack to the bottom third of the oven and preheat the oven to 375 degrees F. Grease the bottom and sides of a rimmed 10-by-15-inch baking sheet with butter.
For the dough: Combine the butter, flour, confectioners' sugar and salt in a food processor and process until the mixture comes together in a solid mass (this may take a few minutes). Drop pieces of the dough all over the prepared baking sheet. Use your fingers to press the dough evenly along the bottom and about 1/2 inch up the sides of the pan, filling any gaps. Set aside.
For the filling: Toss together the peaches, brown sugar, lemon juice, cornstarch, vanilla, cinnamon, salt and nutmeg in a large bowl until the cornstarch dissolves. Transfer the filling onto the crust and spread in an even layer. Bake for 30 minutes.
For the streusel: While the pie bakes, make the strussel topping by combining the flour, almonds, brown sugar, melted butter and salt in a small bowl until evenly moistened.
Remove the pie from the oven and sprinkle the streusel evenly over the filling. Return the pie to the oven and bake until the topping is golden brown and the filling is bubbly, 25 to 30 minutes more. (If the crust browns too quickly during baking, cover the pie loosely with foil.)
Let the pie cool. Serve warm or at room temperature.