To make marshmallow frosting: in a medium bowl, combine cream cheese and marshmallow creme until well combined. Set aside.
Spread a very thin layer of s’mores frosting on the bottom of two graham crackers and place side-by-side on a serving plate.
Top with a layer of marshmallow frosting. Place two graham crackers on top. Then, frost with a layer of s’mores frosting. Place two graham crackers on top. Alternate layers of marshmallow frosting and s’mores frosting between each layer of two graham crackers.
Frost top and sides of the crackers with s’mores frosting. Sprinkle with graham crumbs. Cover with plastic wrap and refrigerate overnight, or for at least 8 hours.
At serving time, cut cake in half down the center, and cut each half into six slices (about 1" thick). Store leftovers in an airtight container in the refrigerator.