In advance: Make cookies. Prepare and roll out dough. For each treat, cut 1 complete cap using cutter from set. Cut 1 mortarboard area only; use knife to trim 1/8 in. off all sides. Bake and cool all cookies.
For complete cap, outline with tip 3 and full-strength icing; flow in center using thinned icing. Let dry. For mortarboard cookies pour on thinned icing to cover. Let dry. Assemble and decorate caps using full-strength icing.
Attach mortarboard to complete cap. Pipe tip 3 rope cording; add tip 2 pull-out tassels. Pipe tip 3 dot button; flatten slightly with fingertip. Pipe tip 1 name. Let all dry. Paint cord and tassel with Pearl Dust; let dry. Attach lollipop stick to back. Let dry.