In a large bowl mix ice cream to soften and place onto a plastic wrap lined casserole dish or baking sheet in an even flat layer. You want the ice cream to be about an inch thick. Cover the dish and place ice cream in the freezer overnight to set.
In a large pot, melt butter over low heat. Add marshmallows and stir until completely melted. Remove from heat and add cereal. Mix until all of the cereal is coated.
Pour cereal mixture into a 13 x 9 x 2-inch pan that's been sprayed with non-stick cooking spray. Let cool.
To assemble sandwiches: Using a square cookie cutter, cut two squares out of the cereal. Next, take the ice cream out of the freezer and cut square out of the ice cream. Sandwich between two marshmallow cereal squares. Serve immediately.