Melt the Chocolate: Combine the chopped baking chocolate and diced butter in a heatproof bowl. Melt over a double boiler or in the microwave in 30-second intervals, stirring until smooth. Let cool slightly.
Prepare the Dry Ingredients: In a medium bowl, whisk together flour, baking powder, salt, and cocoa powder. Set aside.
Mix the Wet Ingredients: In a large bowl, beat the eggs, light brown sugar, vanilla extract, and peppermint extract until combined. Slowly mix in the melted chocolate and butter mixture until smooth.
Combine and Fold: Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Fold in the semisweet chocolate chunks. Cover the dough and refrigerate for 30 minutes.
Bake the Cookies: Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper. Scoop 1 1/2 tablespoon-sized portions of dough onto the prepared baking sheets, spacing them 2 inches apart. Bake for 8-9 minutes, or until the edges are set but the centers remain soft.
Add the Marshmallows: Remove the cookies from the oven and quickly place a marshmallow half on top of each cookie. Return the cookies to the oven for 2-3 minutes, or until the marshmallows puff up slightly.
Finish with Peppermint: Remove the cookies from the oven and sprinkle crushed peppermint candy over the marshmallows while still warm. Let cool slightly.
Optional Drizzle: For an extra indulgent touch, drizzle the cookies with chocolate sauce or melted chocolate chips before serving.