Beat butter and sugar with electric mixer in a large bowl until smooth. Mix in eggs one at a time, beating the first egg in until fully incorporated before adding the second. Stir in vanilla extract.

Sift together flour, cocoa powder, baking soda, and salt in a bowl; stir into butter mixture. Shape dough into a log and wrap with waxed paper, parchment, or plastic wrap. Refrigerate until firm, about 30 minutes.

Preheat oven to 350 degrees F (175 degrees C).

Slice pieces off the log and shape them into narrow wedges about 3 inches long. Set cookies on baking tray. Cut more slices and pull off teaspoon-sized pieces and roll into balls; flatten and press balls onto wide ends of wedges for the mummies' "heads."

Bake in preheated until cookies are set and edges are dry, about 8 minutes. Let cool in pan for 1 minute; remove to wire rack to cool completely.

Combine white chocolate chips with vegetable shortening in a microwave-safe bowl. Heat in microwave on low until melted, 1 to 2 minutes, stirring every 20 seconds, until coating is warm and smooth. Coat the tops of each cookie with melted white chocolate using a small spatula or butter knife. Reheat white chocolate mixture in microwave for a few seconds and stir again if it becomes too thick to work with. Repeat coating remaining cookies with white chocolate.

Use a toothpick to score lines for "bandages" on each cookie, and place mini chocolate chips on the mummy heads for eyes.