In a food processor, pulse 1 1/2 cups of the flour with the granulated sugar and 1/2 teaspoon of salt until blended. Add the butter and pulse until it is the size of peas. Add the water and pulse until the dough is evenly moistened. Transfer the dough to a lightly floured work surface and pat it into a disk. Cover the disk with plastic wrap and refrigerate until chilled, about 30 minutes.
Preheat the oven to 425°. In a medium bowl, toss the peaches with the brown sugar, vanilla, cinnamon, a pinch of salt and the remaining 2 tablespoons of flour.
On a lightly floured work surface, roll out the dough to a 12-inch round. Transfer the dough to a parchment-lined rimmed baking sheet. Mound the peaches with their juices in the center of the dough, leaving a 2-inch border all around. Fold the edge of the dough up and over the peaches. Refrigerate the tart until chilled, about 30 minutes.
Brush the dough with the cream and sprinkle with the turbinado sugar. Bake for about 50 minutes, until the crust is golden and the peaches are bubbling. Let cool for 15 minutes before serving.