Combine flour, cocoa, baking powder, baking soda and salt in bowl; set aside.
Combine 1/2 cup butter and sugar in bowl; beat at medium speed until creamy. Add egg and vanilla; continue beating until well mixed. Add flour mixture; beat at low speed until well mixed.
Divide dough in half. Shape each half into ball; flatten slightly. Wrap each in plastic food wrap; refrigerate at least 2 hours or until firm.
Heat oven to 325°F.
Roll out dough on lightly floured surface, one-half at a time, (keeping remaining dough refrigerated), to 12x7-inch rectangle. (Trim edges if necessary.) Cut rectangle in half lengthwise with pizza cutter or sharp knife. Make 5 crosswise cuts in each half, 2 inches apart, creating 12 (3 1/2x2-inch) rectangles. Place 1 inch apart onto ungreased cookie sheets.
Bake 6-8 minutes or just until set. Cool 1 minute on cookie sheet; remove to cooling rack. Cool completely.
Combine all frosting ingredients in bowl, adding enough half & half for desired spreading consistency. Beat at low speed until well mixed.
Cut licorice twists into 3-inch lengths. Cut slits on 1 end of licorice using sharp knife or kitchen shears to within 1 inch of other end to form tree with 3 or 4 branches. Carefully bend or peel apart branches.
Working with 2 or 3 cookies at a time so frosting doesn’t harden, frost cookies. Place licorice tree onto frosting; sprinkle with Halloween sprinkles or decorator sugars, if desired.