Preheat the oven to 350 F. In a medium bowl, whisk together flour, cocoa powder, salt, and baking soda. In a large bowl, combine the butter and sugar until fluffy.
Add in the egg and vanilla extract, and mix until smooth. Add in the flour mixture, and mix until it is fully combined. Roll the cookie dough into balls, and flatten each slightly.
Place one unwrapped peppermint patty onto each piece of dough. Wrap the dough completely around it and form into a ball. Place the cookies onto a large ungreased baking sheet and bake for 10-12 minutes.
