Combine sliced strawberries and 1/2 cup sugar; stir gently, and chill 1 to 2 hours.
Combine flour, 1/2 cup sugar, baking powder, and salt in a large mixing bowl; cut in 1/2 cup butter until mixture resembles coarse meal.
Combine milk and whole egg; beat well. Add to flour mixture; stir with a fork until a soft dough forms. Pat half of dough out to 1/2 - inch thickness in a greased and floured 9 - inch round cake pan. (Dough will be sticky; dust hands with flour.)
Beat egg white, (at room temperature) until stiff but not dry. Brush surface of dough with half of beaten egg white and 1 tablespoon melted butter.
Roll out remaining dough to 1/2-inch thickness on a lightly floured surface. Place on top of layer in cake pan; trim excess pastry. Brush surface with remaining beaten egg white and 1 tablespoon melted butter.
Bake at 450° for 12 minutes. Remove from pan; while still warm split the two layers and spread each with 1 tablespoon melted butter.
Beat whipping cream until foamy; gradually add powdered sugar, beating until soft peaks form. Place 1 cake layer on serving plate. Spoon on half of whipped cream, and arrange half of sliced strawberries on top. Repeat procedure with remaining cake, whipped cream, and strawberries, reserving some whipped cream. Garnish top of cake with remaining whipped cream and whole strawberries.