Whisk pastry flour, sugar, and salt. Cut in cold butter until pea-size pieces remain, then add ice water until dough holds when squeezed.
Flatten into a disc, wrap, and chill for 1 hour. Heat the oven to 400°F (200°C) and line a rimmed baking sheet with parchment.
Toss sliced peaches with filling sugar, cornstarch, lemon juice, and vanilla just before assembling. Leave the skins on if you like their color.
Roll dough into a 12-inch circle directly on lightly floured parchment. Slide parchment onto the sheet and arrange peaches in the center, leaving a 2-inch border.
Fold the pastry border over the fruit, overlapping as you go. Press folds gently to seal any cracks that could release juices.
Brush only the folded pastry with egg wash and sprinkle with coarse sugar. Leave the center open so moisture can escape.
Bake 35–45 minutes, until pastry is deeply golden and the fruit juices bubble. Rotate once if your oven colors unevenly.
Cool at least 30 minutes on the sheet before slicing. Serve warm or at room temperature with a wide spatula supporting the tender base.
