Prepare the Dough : Preheat the oven to 350°F (177°C) and line two baking sheets with parchment paper. In a large bowl, beat the softened butter, granulated sugar, and brown sugar together until light and creamy. Mix in the egg and vanilla extract until fully combined. In a separate bowl, whisk together the flour, cocoa powder, hot cocoa mix, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, mixing until a thick dough forms. Add the milk and mix until the dough is smooth.
Shape and Bake : Roll the dough into 1.5-inch balls and place them on the prepared baking sheets, spacing them about 2 inches apart. Bake for 10 minutes.
Add Marshmallows : Remove the cookies from the oven and press a marshmallow half, cut side down, into the center of each cookie. Return the cookies to the oven for 2–3 minutes, or until the marshmallows are puffed but not browned.
Melt and Drizzle Chocolate : While the cookies cool slightly, melt the chopped semi-sweet chocolate in a microwave-safe bowl in 20-second increments, stirring after each, until smooth. Spoon or drizzle the melted chocolate over the top of each cookie, covering the marshmallow.
Cool and Serve : Allow the cookies to cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely. Serve and enjoy these warm, gooey delights!