In a medium bowl, whisk together flour, cocoa powder, dry milk powder, baking soda, and salt. Set aside.
In a large bowl, whisk together granulated sugar, brown sugar, and melted butter until smooth. Add egg, egg yolk, and vanilla extract and whisk until thick.
Add dry ingredients to bowl with wet ingredients and mix gently just until combined. Fold in chocolate chips.
Cover bowl and refrigerate dough for 20-30 minutes. While dough is chilling, preheat oven to 350 degrees and line a baking sheet with parchment paper.
Scoop about 2 tablespoon of cookie dough (I use a #40 cookie scoop) onto the prepared baking sheet about 1 ½ inches apart. Bake for about 8 minutes, until edges are set and centers look soft and slightly underdone. Remove baking sheet from oven. Gently press a marshmallow half onto the center of each cookie.
Put baking sheet back in oven and bake for another 2 minutes, until the marshmallows are softened and puffing slightly.
Let cookies cool in the pan for about 5 minutes before moving to a wire rack to cool completely.
Once cooled, drizzle cookies with melted chocolate and add sprinkles.