Pulse the flour, confectioners' sugar, and salt in a food processor until just combined. Add the butter and process until the mixture resembles coarse bread crumbs. Add the ice water gradually and process until the dough holds together when pressed between two fingers. Form the dough into a disk, wrap it in plastic wrap, and chill for 30 minutes.
Preheat the oven to 350 degrees F.
Lightly grease 8 cups of a 12-count muffin pan and line the pockets with strips of parchment paper hanging over the edges. These will help you lift out the tarts.
On a lightly floured work surface, roll out the pastry dough until it is 1/8-inch thick. Cut out 8 pastry circles, and use them to line the muffin pan cups. Cut out 8 additional circles to serve as the tart crust.
In a medium bowl, toss together the cherries, apples, cornstarch and sugar, and spoon the mixture into the pastry cups. Top the tarts with the pastry circles, and crimp the edges together with a fork. Cut a small vent in the top of each of the tarts, brush them evenly with the egg white, and bake until they are golden, about 35 to 40 minutes.