Preheat oven to 350°F. Line a sheet pan with parchment paper.
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar together on medium high speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, mixing after each. Add the vanilla.
In a separate bowl, combine the flour, cocoa powder, baking soda, and salt. Add to the mixer all at once and mix on low until just combined.
Scoop by the rounded tablespoon onto the prepared sheet pan. Roll into balls.
Bake until cookie tops start to crack, about 8 minutes.
Remove from the oven and immediately top each cookie with a marshmallow. Return the pan to the oven and bake an additional 2 minutes. Remove cookies from the oven and use your fingers to flatten the marshmallows a little. Let cool completely.
Place the chopped chocolate in a heat proof bowl and set over a pan of barely simmering water. Let chocolate melt, stirring frequently, and remove as soon as no lumps remain. Use a spoon to cover each cooled cookie with chocolate. Put in the fridge to firm up.
Store cookies in an airtight container at room temperature. Cookies are best if consumed the day they are made, but will keep for several days.