In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the softened butter, granulated sugar, and brown sugar together on medium-high speed until fluffy and light in color, about 2–3 minutes. Add the egg and vanilla extract, and beat on high speed until combined. Scrape down the sides and bottom of the bowl as needed.
In a separate bowl, whisk the flour, cocoa powder, hot cocoa mix, baking soda, and salt together until combined. Add the dry ingredients to the bowl with the wet ingredients. Beat on low speed until combined. The cookie dough will be thick. Finally, beat in the milk. The cookie dough will be thick and sticky.
Cover the dough tightly and chill in the refrigerator for at least 2 hours and up to 3 days. Chilling is imperative for this sticky cookie dough.
Preheat the oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats. Set aside.
Remove the cookie dough from the refrigerator. Scoop and roll dough, using a heaping 1 tablespoon (about 25-26g) per cookie, into balls. Arrange 2–3 inches apart on the prepared baking sheets.
Bake the cookies for 10 minutes. Remove the cookies from the oven and lightly press a marshmallow half into the tops of each cookie. Return them to the oven and bake for an additional 2 minutes. Remove from the oven and, using the back of a spoon, gently press down on the marshmallow to slightly flatten it.
Allow the cookies to cool on the baking sheet for 10 minutes, then transfer to a wire rack to cool completely.
Melt the chocolate: You can melt the chocolate in a double boiler or the microwave. If using the microwave, place the chopped chocolate in a medium heat-proof bowl. Microwave in 20-second increments, stirring after each increment until completely melted and smooth.
Spoon the melted chocolate over each cooled marshmallow-topped cookie. Place the cookies back on a baking sheet or leave them on the wire rack to allow the chocolate to set at room temperature for 30-60 minutes. Once the chocolate has set, the cookies can be stacked, stored, transported, and gifted.
Store leftover cookies tightly covered at room temperature for up to 1 week.