Make the tart dough: Combine the flour, sugar, and salt in a food processor and pulse to blend. Add the butter and pulse until the mixture forms coarse crumbs. Stir together the 1/4 cup ice water and the vanilla; sprinkle the water over the mixture in the processor and pulse just until a dough forms, adding a little extra ice water if necessary. Divide the dough in half, and shape each half into a 1-inch-thick round. Wrap 1 disk tightly in plastic wrap and refrigerate for at least 1 hour; freeze the other for a future use.

Put a pizza stone in the oven and preheat the oven to 425ºF for 45 minutes. Remove the dough from the refrigerator about 15 minutes before rolling to soften it slightly.

Place the dough round between 2 sheets of parchment paper and roll into a 13-inch round, flouring the round lightly as needed to keep the dough from sticking. Remove the top sheet of parchment. Slide a pizza peel or rimless baking sheet under the bottom sheet of parchment.

Make the filling: Combine the cherries, sugar, flour, and cinnamon in a bowl and toss well. Fill the center of the dough round with the cherries in an even layer, leaving a border of about 1 1/2 inches. Fold the border up and over the cherries to make a rim. Brush the rim with egg wash, then sprinkle with coarse sugar. Trim the excess parchment with scissors.

Use the pizza peel or baking sheet to transfer the crostata, still with parchment underneath, to the oven, sliding it, with the paper, directly onto the pizza stone. Bake until the crust is nicely browned and the cherries are bubbling, about 40 minutes. Remove from the oven with the peel or baking sheet and let cool on a rack for 15 minutes before serving. Serve warm.