Preheat the oven to 350℉ and line a baking sheet (also known as a cookie sheet) with parchment paper.
Brown butter over medium heat in a medium saucepan. (Melt while whisking and continue cooking until foamy on top and golden brown.) Turn off the heat.
Add graham crumbs and whisk until smooth.
Add granulated sugar and brown sugar. Whisk until smooth. The mixture will look like wet sand. Take off heat and transfer the mixture to a large bowl.
Add the ice. Once it's melted, whisk the mixture until smooth.
Add egg and vanilla extract. Whisk until smooth.
Add flour, espresso powder, cinnamon, baking soda, salt. Fold with a spatula until there are no large streaks of flour.
Mix in the chocolate chips until just combined.
Top a graham cracker half with chocolate and marshmallow. Then scoop a 1/4 cup cookie dough ball and place on top. Repeat for all 8 cookies.
Place onto the baking sheet 1-2 inches apart. Bake for 10 minutes or until the edges of the cookie look dry. The inside of the cookies will still be soft, but they will set as they cool.
Leave the cookies on the baking sheet or on a wire rack until they're cool before storing in a container so they don't get soft from enclosed steam.