In a large bowl, whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl using a handheld mixer), beat the butter, brown sugar, and granulated sugar until smooth. Mix in the egg and then the vanilla until well combined, scraping down the sides of the bowl as needed.
Slowly add the dry ingredients to the wet ingredients and mix until just combined.
Cover and refrigerate dough for at least 30 minutes.
Preheat oven to 350°F. Line two large baking sheets with parchment paper and set aside.
Remove the dough from the refrigerator and scoop out 2-2.5 tablespoon sized pieces of dough onto the baking sheet.
Flatten each piece of dough, press a peppermint patty into the center, then fold the dough around the patty making sure it is completely closed inside the dough.
Bake at 350°F for 10-12 minutes.
Remove from the oven and cool on the baking sheet for 10 minutes, then transfer to a wire rack to finish cooling.
Cookies may be stored in an airtight container on the counter for up to five days.