Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and salt in a food processor; pulse 2 times. Add 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 mixture 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 with 2 additional lengths of overlapping plastic wrap. Roll the dough, still covered, into a 14-inch circle. Place dough in freezer 5 minutes or until plastic wrap can be easily removed. Remove bottom sheets of plastic wrap. Place dough into a 10-inch tart pan, pressing dough against sides of pan and allowing it to extend over edge of pan. Remove top sheets of plastic wrap.
Preheat oven to 425º.
Arrange half of the apple slices in the bottom of the tart pan, and sprinkle with half of the sugar. Repeat the procedure with the remaining apple slices and sugar. Fold the dough over the apple slices (dough will partially cover apple slices). Brush dough with egg white. Place pan on a baking sheet.
Bake at 425º for 45 minutes or until apple is tender and crust is lightly browned (shield tart with foil if it becomes too brown). Cool on a wire rack.