Combine flour, cocoa powder, sugar, salt and baking soda in the bowl of a food processor with the dough blade. Pulse to combine. Add butter slowly to form a crumbly mixture. With the food processor running, drizzle in cream and vanilla.
Turn onto a lightly floured surface and form into a log. Cover and refrigerate for at least 30 minutes.
Preheat oven to 350 degrees. Line a baking sheet with parchment paper.
Slice cookies to desired thickness. Bake cookies for 8 to 10 minutes.
Allow cookies to cool completely.
In the top of a double boiler, add white chocolate and butter. Cook over medium-low heat until the chocolate is completely melted, stirring often. Remove from heat and spread over the top of the cookies. Top with peppermint and allow to sit until the chocolate is set.