Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats so the cookies do not stick.
In a large mixing bowl, beat the softened butter and brown sugar together until the mixture is light and fluffy. This should take about 2 to 3 minutes using an electric mixer.
Mix in the egg and the molasses. Beat well until the mixture is smooth and fully combined. Be sure to scrape down the sides of the bowl as needed.
In a separate medium bowl, whisk together the flour, cocoa powder, ground ginger, cinnamon, cloves, baking soda, and salt. Ensure there are no large lumps of cocoa powder.
Gradually add the dry ingredients to the wet ingredients. Mix on low speed until just combined. Fold in half of the chocolate chips by hand.
Scoop rounded tablespoons of dough and place them 2 inches apart on the prepared baking sheets. Bake for 8 minutes.
Remove the sheets from the oven. Quickly press a few mini marshmallows and the remaining chocolate chips into the top of each warm cookie. Return to the oven for another 2 minutes, or until the marshmallows are slightly puffed and the cookies are set.
Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. This helps the bottoms firm up without overcooking.