Preheat oven to 400°.
Cut asparagus spears 4 inches from tips; reserve tips. Coarsely chop remaining asparagus; set aside.
Combine egg whites and egg in a medium bowl, stirring with a whisk. Add milk, salt, nutmeg, and pepper. Stir in chopped asparagus.
Place 1 phyllo sheet on a large cutting board or work surface (cover the remaining dough to prevent drying); lightly coat with cooking spray. Repeat layers with remaining phyllo and cooking spray, ending with phyllo. Gently press phyllo layers together. Lightly coat top phyllo sheet with cooking spray.
Cut phyllo stack into an 11-inch circle using a sharp knife; coarsely chop excess dough. Carefully place phyllo circle into a 9-inch tart pan coated with cooking spray; gently press phyllo into pan. Fold edges over. Sprinkle chopped dough over phyllo circle; top with 1/4 cup cheese and potato. Place tart pan on a foil-lined baking sheet. Pour egg mixture into tart shell. Arrange asparagus spokelike on top of egg mixture with tips toward outside of pan, and sprinkle evenly with 1/4 cup cheese. Bake at 400° for 20 minutes. Loosely cover tart with foil. Bake an additional 5 minutes or until tart is set.