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1
Chill a large mixing bowl and beaters in refrigerator for at least 1 hour. Add cream cheese to the bowl and beat on medium-high speed until smooth. Add heavy cream and beat on medium-high speed until soft peaks form. Fold in marshmallow creme and vanilla until well mixed. Refrigerate until ready to use.
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2
Crush 1 sheet of graham crackers in a food processor and set aside.
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3
Remove 2 to 3 tablespoons of the frosting to a small microwave-safe bowl and set aside. Place remaining frosting in another microwave-safe bowl and microwave on high for 30-35 seconds, stirring every 10-15 seconds. Stir until completely smooth. Let frosting stand for 3-4 minutes.
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4
In the center of a large platter, spread a thin layer of the marshmallow whipped cream into approximately an 8 x 8 inch square. (It does not have to be exact; you just want to be slightly larger than the 7 1/2 inch square needed for the icebox cake.)
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5
Place a half sheet of graham cracker in the center of the whipped cream square. Using four full sheets of graham crackers, create a square around the half-sheet of graham cracker by placing crackers end-to-end.
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6
Spread melted frosting (about 1/4 to 1/3 cup) over the graham crackers with a small offset spatula to cover. It's perfectly fine if some of the frosting dribbles over the edge. Spread about 1/4 of the remaining marshmallow whipped cream over the frosting layer from edge-to-edge.
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7
Repeat the graham cracker/frosting/whipped cream layering three more times. Sprinkle the reserved crushed graham crackers evenly over the top whipped cream layer.
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8
Melt the 2 to 3 tablespoons of reserved frosting in the microwave on high for 10 seconds. Stir until smooth and transfer to a small plastic bag. Snip off a small piece from the corner of the bag and drizzle the melted frosting over the cake.
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9
Refrigerate for 24 hours prior to serving.
