Cream shortening in a large mixing bowl; gradually add sugar, beating until light and fluffy. Add vanilla and salt; beat well. Add 4 eggs, one at a time, beating well after each addition. Press hard-cooked egg yolks through a sieve into creamed mixture, stirring well.
Add flour to creamed mixture alternately with whipping cream, beginning and ending with flour. Stir well after each addition. Cover and chill several hours or overnight.
Work with one-fourth of dough at a time, keeping remaining dough chilled until ready to use. Roll to 1/4-inch thickness on a well-floured surface, and cut into 2-inch squares. Place 1/4 teaspoon orange marmalade in center of each square. Fold dough into a triangle, and press edges together with a fork. Brush tops with egg white.
Place 2 inches apart on lightly greased cookie sheets. Bake at 350° for 15 minutes or until lightly browned. Remove to wire racks to cool. Repeat procedure with remaining dough, marmalade, and egg whites.