Preheat oven to 325ºF (160ºC). Line baking sheets with parchment paper.
Cookies: Cream butter, sugar and vanilla in a large mixing bowl, 1 to 2 minutes. Add flour and cocoa and mix on low speed, scraping the bowl frequently, until dough comes together.
Divide dough into 4 pieces. On a lightly floured surface, roll each piece to a ¼” (5 mm) thickness. Cut out shapes using a 2” (5 cm) cookie cutter. Gather up scraps and repeat with remaining dough. Place on prepared baking sheets.
Bake in preheated oven for 18 to 20 minutes. Cool on racks 30 minutes. Dip into melted chocolate.