Preheat oven to 350˚F (180˚C).
In a food processor, add the graham crackers and process until fine. You can also crush the crackers in a Ziploc bag with a rolling pin. Transfer the crumbs to a medium bowl. Add sugar and mix to combine. Add the melted butter and mix well. Scoop enough crumbs to fill each mini muffin tin. Press the mixture firmly onto the bottom of the tins with the help of the back of a tablespoon measuring spoon. Bake in the oven for 5 minutes. Remove from oven and cool on a cooling rack.
Meanwhile, work on the ganache. Set a medium heatproof bowl over a pot of simmering water. Make sure the water is not touching the bottom of the bowl. Add heavy cream, instant coffee powder and chocolate chips into the bowl. Stir until the chocolate is melted. Remove from heat and stir for a few more times. Scoop enough ganache to fill the graham cracker cups about ¾ full.
Change the oven setting to broiler. Move the rack if needed (see tip 2 below).
Place half a marshmallow on top of each ganache cups. Transfer to the broiler and bake for 5 – 20 seconds or until the marshmallow is golden brown. DO NOT walk away. Marshmallow can get burnt in a matter of seconds.
Once they are out of the oven. Immediately place the chocolate pieces on top of the marshmallow and press down slightly. Let the cups cool in the pan for at least 1½ hour. Run a sharp knife around the edge of the cups and carefully remove them. Place them on mini cupcake liners. Serve at room temperature or microwave them for 4 seconds.