Buttermilk Pie Dough:
1 2/3 cups all-purpose flour, plus additional for dusting
2 teaspoons sugar
1/4 teaspoon fine salt
1/2 cup (1 stick) cold unsalted butter, cut into small cubes
1/4 cold buttermilk, well-stirred
4 tablespoons pure cane sugar
1/2 vanilla bean, split lengthwise and seeds scraped out
Finely grated zest of 1 lemon plus 1 tablespoon juice
½ pound sliced fresh peaches
½ pound sliced fresh plums
1 tablespoon cornstarch
1 tablespoon buttermilk
1 tablespoon turbinado sugar
1 tablespoon prepared jam, such as apricot or peach thinned with 1 tablespoon of water
1. Make the buttermilk pie dough: In a food processor, combine the flour, sugar, salt, and butter. Pulse until the mixture resembles coarse meal. Add half of the buttermilk and pulse until the dough starts coming together to form crumble-like pieces, adding additional buttermilk, 1 teaspoon at a time if needed. Transfer the dough to a large piece of plastic wrap, use your hands to bring the dough together then pat into a 1-inch disk and wrap tightly. Chill in the refrigerator until the dough is completely firm, at least 1 hour and up to 2 days.
2. Make the peach-plum filling: In a medium bowl, combine 2 tablespoons of pure cane sugar, the vanilla beans, and lemon zest. Use your fingers to rub the mixture together to infuse the sugar with the vanilla and lemon. Add the sliced fruit and gently toss to coat. Set aside while you roll out your dough.
3. Set an oven rack in the lowest position and preheat the oven to 375ºF. Line a large rimmed baking sheet with parchment paper and set aside. Remove the dough from the refrigerator and let it sit at room temperature to soften up a bit, about 10 minutes. Lightly dust a work surface with flour and roll out the dough into a 1/8-inch round approximately 12-inches around. Transfer the dough onto the prepared baking sheet.
4. Gently stir the lemon juice into the fruit then sprinkle with the remaining 2 tablespoons of sugar and the cornstarch. Gently mix with your hands and toss to coat. Spread the fruit out onto the dough leaving a 2-inch border. Fold the edges over the filling, pleating as you go and leaving the center of the crostata uncovered. Using a pastry brush, lightly brush the edges of the dough with the buttermilk and sprinkle with the turbinado sugar. Using the same pastry brush, gently brush the top of the fruit with the jam mixture.
5. Bake until the crust is deeply golden brown and the filling is bubbling and thickened, 45 to 55 minutes. Allow the crostata to cool on the baking sheet for 30 minutes.