Preheat oven to 350º.

Combine flour, cocoa, baking soda, and salt, stirring well with a whisk.

Place shortening in a large mixing bowl; beat with a heavy-duty mixer at medium speed until light and fluffy.

Gradually add the granulated sugar, 1 tablespoon at a time, beating until well blended.

Add vanilla and egg white; beat well.

Add flour mixture; beat until well blended.

Turn dough out onto wax paper; shape into a 6-inch log.

Wrap log in wax paper.

Freeze 2 hours until very firm.

Cut log into 1/4-inch slices, and place slices 1 inch apart on baking sheets coated with cooking spray.

Bake at 350º for 7 minutes. These will harden as they cool, so do not over bake.

Remove from pans; cool completely on wire racks.

Combine powdered sugar and milk in a medium bowl; stir well with a whisk until smooth.

Spoon into a small zip-top plastic bag; seal.

Snip a tiny hole in 1 corner of bag.

Working with 1 cookie at a time, pipe 2 to 3 circles onto each cookie.

Starting at center circle, pull a wooden pick through other circles at regular intervals to create a "web."

Note: For the glaze, snip a very small hole in the corner of the plastic bag. If it's too small, you can always make it bigger.