Preheat oven to 350°F. Line a large baking sheet with parchment paper.
In a medium bowl, mix together flour, baking powder, baking soda, ground coffee and salt; set aside.
In the bowl of an electric mixer, cream together peanut butter, butter and both sugars until combined. Add eggs and beat well until fluffy. Stream in the flour mixture and mix until thoroughly combined. Scoop out batter by the tablespoonful. Bake until golden around the edges, about 11 to 13 minutes (may take longer if you bake two sheets at the same time). Remove sheet from oven and let cool on wire rack.
To prepare topping, place marshmallows, in a single layer, on a foil-lined baking sheet. Lightly brown marshmallows by toasting them under a broiler for a few minutes until they get golden brown (alternatively, use a kitchen torch).
In a coffee grinder (or the bowl of a food processor), pulse graham crackers and ground coffee together; set aside.
In a small bowl, melt chocolate chips in the microwave for about 1 minute on high (or over a double boiler); set aside.
Dip the edge of each cookie into the melted chocolate and then take 2 marshmallows per cookie and press them into the melted chocolate before it hardens.
Working quickly while the chocolate is soft, dust cookie with some graham crumbs.
Store cookies in an airtight container for a week (freezing will change the texture so it is not recommended).