Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, cocoa powder, and baking soda until combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Chill the dough in the refrigerator - covered - for an hour minimum.
Using a cookie scoop or spoon, drop 2T sized balls of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Pull the cookie dough balls apart in the middle to place one half of a Milky Way bar into the center. Fold the cookie dough back around the candy bar to cover completely.
Sprinkle cookies with sea salt. Bake in the preheated oven for 9 minutes.
Allow the cookies to cool on the baking sheets for 5 minutes before transferring them to wire racks to cool completely.