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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°F.
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°F for 20 minutes.
Reduce oven temperature to 375°F; bake an additional 30 minutes or until pie is golden brown.
Cool completely on a wire rack.