For the dough:

Line a cookie sheet with parchment paper so it lies flat on the pan. Set aside until needed. Adjust oven rack to the lower-third level and preheat oven to 425°F.

Add the flour to the bowl of a food processor fitted with a metal blade. Remove the cold butter from the refrigerator, and cut into about ¼"-wide slices. Add the cold butter and salt on top of the flour, place cover securely on top and pulse twice to coat the butter chunks with flour.

Process continuously until a coarse meal has formed. The mixture should feel cool and slightly grainy, like cornmeal. If there are still large pieces of isolated butter, then you need to process a little bit more, but be careful not to overmix, which would be beyond the coarse-meal stage.

Once the meal is coarse, remove the cover. In a small bowl, beat the yolk with the 3 tablespoons cold water until smooth. Pour over the top of the coarse meal halfway between the side of the bowl and the center blade. Place the cover on top and continue processing only until a ball forms and rolls around in the bowl twice. Stop the processor.

Lightly dust the top of a smooth counter with extra all-purpose flour. Turn the dough out onto center of the dusted counter. Dust the top of the dough lightly with flour from sifter. Knead the dough gently and quickly, just until smooth. Dust lightly with additional flour only as needed to prevent the dough from sticking to the table and your hands.

Form dough into a round disc with smooth edges, about 6 inches in diameter. Place the disc of dough on the center of the flour-dusted counter. Keep the counter and top of dough lightly dusted with flour while rolling. Occasionally glide your hand under the dough and rotate it in a circle to ensure it is not sticking to the counter. If the dough begins to stick to the counter or rolling pin, that’s when you want to dust with more flour. Roll the dough into a 12" circle. Using a dry, soft 3-"-wide bristle pastry brush, brush off any extra flour from the dough.

Roll the dough around the rolling pin and unroll on parchment-lined cookie sheet.

In a small bowl, beat the egg white until smooth. Dip a small pastry brush into the egg white. Paint a thin layer of beaten egg white over the top of the rolled dough. Save the extra beaten egg white for use later.

For the filling:

Wash the peaches in cold water and towel dry. Cut into ½"-thick slices. Place slices in a large bowl. In a small bowl, combine the sugar and tapioca, stir together until evenly blended. Sprinkle tapioca and sugar mixture over the peaches. Using a rubber spatula or large kitchen spoon, fold only until the fruit is covered.

Add the peaches to the center of the dough and evenly spread, leaving about a 2½" border. Gently press the peaches to close any large gaps between the slices.

Glide your hand under the edge of the dough, about 2½" in, and fold halfway toward the center of the filling. Continue this motion, making a pleat as you fold each piece of the edge until you have finished and created an outer edge with an open center. Once done, lightly paint the top ring of folded dough with egg white. Place in the preheated oven on the lower third rack.

After 30 minutes, remove from the oven. Using the back of a large oval soup spoon, gently press peaches down to the level of the juices. This will give a simple glaze to the top of the peaches. Return to the oven and reduce heat to 400°F. Continue baking another15–20 minutes, until the fruit is tender and the crust is golden brown. Place the pan on a wire rack for even cooling.