Combine 1/4 cup flour and ice water, stirring with a wire whisk until well-blended; set aside. Combine remaining flour, sugar, and 1/4 teaspoon salt in a bowl; cut in shortening with a pastry blender or 2 knives until mixture resembles coarse meal. Add ice water mixture; mix with a fork until dry ingredients are moistened. Gently press mixture into a 4-inch circle on heavy-duty plastic wrap, and cover with additional plastic wrap. Roll dough, still covered, into an 11-inch circle; chill 10 minutes or until plastic wrap can be easily removed.
Remove 1 sheet of plastic wrap; fit dough into a 10-inch round tart pan coated with cooking spray, and remove top sheet of plastic wrap. Prick the bottom and sides of dough with a fork, and bake at 400° for 15 minutes. Let cool on a wire rack.
Combine pumpkin and next 8 ingredients (pumpkin through egg whites) in a bowl; stir well with a wire whisk. Pour into prepared crust; bake at 350° for 40 minutes or until filling is almost set. Let cool 30 minutes on a wire rack; cover loosely, and chill at least 4 hours.
Uncover and press the brown sugar through a small wire sieve onto filling. Shield edges of piecrust with aluminum foil; broil 1 minute or until sugar is bubbly. Serve immediately.