Step 1

Cream butter and confectioners' sugar until light and fluffy, 5-7 minutes. Add chocolate, egg and vanilla; mix well. In another bowl, whisk together flour, baking soda, cream of tartar and salt; gradually add to creamed mixture, beating well. Divide dough in half; shape each half into a 2-in.-diameter roll. Wrap in waxed paper; refrigerate until firm, about 1 hour.

Step 2

Preheat oven to 400°. Unwrap dough and cut crosswise into 1/8-in. slices. Place 2 in. apart on ungreased baking sheets. Bake until edges are firm, 7-8 minutes. Remove from pans to wire racks to cool completely.

Step 3

Combine all frosting ingredients; beat until smooth. Spread over cookies; let dry completely. Store in airtight containers.