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. Add vanilla and water to processor, then slowly add flour and cinnamon sugar. 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 future use.
Put a pizza stone or cookie sheet in the oven and preheat the oven to 425 degrees F 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 (about a 1/4-inch thickness), flouring the round lightly as needed to keep the dough from sticking. Remove the top sheet of parchment. Use the rim of a small round bowl to make 6 individual crostatas. Cut around the edge of the bowl, in the dough, with a sharp knife. Slide a pizza peel or rimless baking sheet under the bottom sheet of parchment, and remove excess dough from crostatas.
To make the filling, combine the apples, sugar, flour, and cinnamon in a bowl and toss well. Add cranberry sauce and salt and toss again, briefly. Paint the edges of the crostatas with egg yolk wash. Fill the center of the dough rounds with the apples (about 1/2 cup each) in an even layer, leaving a border of about 1 1/2 inches. Fold the border up and over the apples to make a rim. Brush the rim with egg wash, then sprinkle with coarse sugar. Trim the excess parchment with scissors, and press sides together.
Use the pizza peel or baking sheet to transfer the crostatas, 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 apples 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. Note: This can be made hours ahead and reheated before serving.
Every region has its own best baking apples. Be sure to talk to your green grocer to find out what's best near you!
Recipe courtesy Michael Chiarello