In a large saucepan over low heat, melt the butter and marshmallows together, stirring until smooth. Remove from heat.
Add the Rice Krispies cereal to the melted mixture. Stir until all the cereal is well-coated.
Press the Rice Krispie mixture firmly into the bottom of a 9-inch springform pan to form an even layer. Set aside to cool.
In a mixing bowl, combine the softened cream cheese, powdered sugar, and vanilla extract. Using a hand mixer, beat until the mixture is creamy and smooth.
Gently fold the whipped topping into the cream cheese mixture until fully incorporated.
Pour the cheesecake filling over the cooled Rice Krispie crust, smoothing the top with a spatula.
Refrigerate the cheesecake for at least 4 hours, or until set (overnight is recommended).
Once set, carefully remove the sides of the springform pan. Garnish with additional Rice Krispies if desired before serving.