To prepare crust, lightly spoon flour into dry measuring cups; level with a knife. Combine flour and salt, stirring well with a whisk. Cut in 5 tablespoons butter and shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add water, stirring just until moist. Divide dough into two equal portions. Gently press each portion into a 4-inch circle on a sheet of plastic wrap; cover. Chill 30 minutes.
Preheat oven to 425°.
Unwrap dough; place 1 portion chilled dough on a lightly floured surface. Roll dough into a 12-inch circle. Fit dough into a 10-inch deep-dish pie plate coated with cooking spray.
To prepare filling, combine 2/3 cup brown sugar and cornstarch in a large bowl, stirring well with a whisk. Add mango; toss to coat. Add mango mixture to prepared pie plate; sprinkle evenly with 1 tablespoon butter.
Unwrap dough; place remaining chilled dough portion on a lightly floured surface. Roll dough into a 12-inch circle. Fit dough over mango mixture. Press edges of dough together. Fold edges under; flute. Cut several slits in top of dough to allow steam to escape.
To prepare topping, brush top of dough with milk. Combine ginger and granulated sugar; sprinkle evenly over dough. Place pie plate on a foil-lined baking sheet; bake at 425° for 20 minutes. Reduce oven temperature to 375°; bake an additional 30 minutes or until pie is golden brown. Cool completely on a wire rack.