Blend the Oreo cookies in a food processor until varied sizes. Sift together flour, cocoa powder, baking soda, and salt in a bowl.

Beat melted butter, brown sugar, and granulated sugar until pale and fluffy. Mix in vanilla extract and eggs until smooth.

Gradually incorporate dry ingredients into wet mixture. Fold in Oreo pieces and crumbs gently.

Preheat oven to 350°F (175°C) and line baking sheets with parchment paper. Rest cookie dough at room temperature for 10 minutes.

Using a cookie scoop, place 6 dough balls per baking sheet. Bake for 12-14 minutes until set around edges.

Cool cookies on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Beat softened butter for frosting until creamy. Add sifted powdered sugar and cocoa powder, mixing until smooth. Stir in vanilla and salt.

Frost each cooled cookie generously and sprinkle with extra Oreo crumbs and place gummy worms on top.