Making the Delightful Cookies:
In a medium saucepan or a microwave-safe bowl, gently melt the butter and chocolate together, stirring often until smooth. Set this rich mixture aside to cool slightly.
In a separate medium bowl, whisk together the flour, cocoa powder, baking powder, and salt.
Using an electric mixer, beat the brown sugar, eggs, and vanilla extract on low speed until beautifully combined.
Carefully add the slightly cooled chocolate mixture to the egg mixture, blending just until everything is incorporated.
Slowly add the dry flour mixture, mixing only until just combined to keep the cookies tender.
Scrape down the sides of the bowl, then cover the cookie dough and refrigerate it for at least 1 hour until it’s firm. If you make the dough a day ahead, let it sit at room temperature for about 30 minutes before shaping.
Preheat your oven to 325°F and line two baking sheets with parchment paper or a silicone mat.
Scoop tablespoon-sized portions of dough (a cookie scoop works great!), roll them into smooth balls with your hands, and arrange them about 2 inches apart on the baking sheets. Gently flatten each ball.
Bake the cookies for about 12 minutes.
While the cookies bake, prepare your marshmallows by cutting each large marshmallow in half crosswise.
Once the cookies are out of the oven, immediately press one marshmallow half (cut side down) into the center of each warm cookie.
Return the cookies to the oven for another 2-3 minutes to slightly toast the marshmallows.
Allow the cookies to cool on the baking sheet for a few minutes, then transfer them to a wire rack to cool completely.
Preparing the Dreamy Icing:
In a medium bowl, combine all the icing ingredients and whisk until you have a smooth, luscious fudge glaze.
Place your wire cooling rack (with the cooled cookies) over a baking sheet to catch any excess icing.
Spoon a small amount of icing onto the top of each marshmallow, spreading it gently with the back of the spoon.
After icing just a couple of cookies, quickly add your favorite sprinkles before the icing sets.
Allow the icing to set for about 30 minutes before serving these delightful, homemade hot cocoa cookies!