Combine the first 4 ingredients in a medium bowl; cover and let stand for 1 hour. Drain.
Preheat oven to 425°.
Lightly spoon flour into dry measuring cups; level with a knife. Place flour, 1 tablespoon granulated sugar, and salt in a food processor; pulse 2 times or until combined. Add chilled butter; pulse 4 times or until mixture resembles coarse meal. With processor on, add ice water through food chute, processing just until combined (do not form a ball). Gently press dough into a 4-inch circle on plastic wrap; cover. Chill for 15 minutes.
Slightly overlap 2 lengths of plastic wrap on a slightly damp surface. Unwrap chilled dough, and place on plastic wrap. Cover the dough with 2 additional lengths of overlapping plastic wrap. Roll dough, still covered, into a 14-inch circle. Place dough in freezer 10 minutes or until plastic wrap can be easily removed. Remove the top sheets of plastic wrap; fit dough, plastic wrap side up, into a 10-inch round removable-bottom tart pan coated with cooking spray. Press dough against bottom and sides of pan, allowing dough to extend over edges of pan; remove remaining sheets of plastic wrap.
Combine 3 tablespoons granulated sugar, brown sugar, and cornstarch; stir with a whisk. Sprinkle 1/3 cup cornstarch mixture into pastry shell; cover with half of fruit mixture. Repeat layers with the remaining cornstarch mixture and fruit mixture. Fold edges of dough over fruit mixture (dough will only partially cover fruit). Sprinkle 2 tablespoons granulated sugar over fruit mixture; bake at 425° for 20 minutes. Reduce oven temperature to 350° (do not remove galette from oven), and bake for an additional 45 minutes or until the pastry is golden. Cool for 10 minutes on a wire rack, and sift the powdered sugar over the top of the galette. Serve the galette warm or at room temperature with whipped topping.