Line a 9x5-inch loaf pan with plastic wrap where enough hangs over the sides to cover the top of the cake once it's assembled. Spray the plastic wrap with non-stick cooking spray.
In a large bowl, stir together the crushed cereal and melted butter until well combined. Press 1 ½ cups of the cereal mixture into the bottom of the prepared loaf pan.
Spread 2 cups softened chocolate ice cream over the cereal layer. Sprinkle with ⅓ of the chopped chocolate chunks.
In a large bowl, stir together the mini marshmallows and thawed whipped topping. Spread half over the top of the chocolate chunks layer. Sprinkle with ½ cup marshmallow bits.
Repeat layers with 1 ½ cups cereal, remaining chocolate ice cream, half of the remaining chocolate chunks and remaining marshmallow whipped topping mixture. Reserve the remaining marshmallow bits for the very top of the cake.
Sprinkle the remaining cereal over the marshmallow whipped topping layer. Sprinkle the remaining chocolate chunks over the cereal and then the remaining marshmallow bits over the chocolate chunks.
Pull the plastic wrap that's hanging over the sides of the pan to loosely cover the top of the cake. Place cake in the freezer for at least 4 hours.
When ready to serve, lift cake from the pan using the sides of the plastic wrap. Cut into slices with a large sharp knife and serve. Store leftover cake in the freezer.