Wash, peel, and finely dice peaches. Mix together with sugar and cornstarch. Heat the peach mixture on medium-low and simmer until thickened, 5 to 7 minutes. Set aside to cool.

Roll the puff pastry into a 9×15 rectangle. Cut the pastry into 8 equal squares for mini turnovers, or 6 squares for larger turnovers.

Preheat the oven to 425.

When the peach mixture has cooled, spoon 1-2 tablespoons of peaches onto the puff pastry squares, off center. Fold the pastry over the filling to make a triangle and seal the perimeter by pinching the edges or pressing the tines of a fork into the dough. Place the turnovers on a baking sheet and brush with the egg white.

Bake until the dough is crispy and golden brown, 12 to 15 minutes.