In a large bowl, beat together the butter and sugar on high speed until light and fluffy, about 3 minutes. Add in the egg, milk, and vanilla and mix until combined.
In another bowl, whisk together flour, cocoa powder, baking soda, and salt. Add to the butter mixture and mix until fully combined. Stir in the pecans by hand.
Drop rounded tablespoons of dough on an ungreased cookie sheet, leaving 2 inches between them. Bake for 6 minutes before removing from the oven. Press a marshmallow into the center of each cookie and return the pan to the oven. Bake 2-3 minutes longer until the marshmallows are soft and the edges of the cookies are set.
Remove the cookies from the oven and let them cool for a minute or two on the pan before transferring them to a cooling rack to cool completely.
Add the chocolate chips to a small microwave-safe bowl and melt in 30-second increments, stirring between each increment until smooth.
Pour the melted chocolate into a ziplock bag and snip the corner. Drizzle over the top of the cooled cookies.