Preheat oven to 375 degrees F.
Prepare a baking sheet by lining it with parchment paper. Set the uncooked pie dough onto the baking sheet.
In a bowl, gently mix peaches, sugar, and flour together. Pour fruit mixture into the center of the pastry round, leaving about 2 1/2 inches around the edge. Fold up the edge of the pastry dough over the filling to make a rim. Fan the edge as you go around folding the dough.
Brush pastry with the beaten egg and place the pat of butter on top of the fruit mixture. Bake for 30 to 45 minutes or until the pastry is golden brown and the fruit is bubbling. Cool the crostata on a rack and serve warm or at room temperature with your favorite ice cream.