Cream butter, brown sugar, and white sugar on medium speed for 2-3 minutes until light, fluffy, and creamy.
Add egg, milk, and vanilla. Mix on low until smooth (the batter may look curdled briefly).
In a separate bowl, whisk together flour, cocoa powder, baking soda, and salt.
Add dry ingredients to wet mixture. Mix on low just until flour disappears. Do not overmix.
Fold in 50g of chopped chocolate (save the other 50g for topping).
Divide dough into 6 equal portions (80-90g each). Gently roll into balls, then flatten slightly to about 1 cm thick.
Freeze dough balls on a tray for 15 minutes.
Preheat oven to 175°C (350°F). Place frozen dough balls on a lined baking sheet, spaced 5 cm apart. Bake for 7 minutes.
Remove from oven and gently press the center of each cookie to create a shallow well.
Cut 5 large marshmallows in half. Place one half (cut side down) into the well of each cookie.
Return to oven and bake for 2-3 minutes until marshmallows are puffed and golden.
Cool on baking sheet for 5 minutes, then transfer to a wire rack to cool completely.
Melt half of the remaining 50g chocolate. Stir in the other half (unmelted) until smooth (tempering).
Drizzle tempered chocolate over cooled cookies. Let sit at room temperature until firm.