Prepare the Creamy Lime Filling

1. Whip the Cream: In a large mixing bowl, whip the chilled heavy cream until stiff peaks form. This usually takes about 2-3 minutes with an electric mixer.
2. Mix the Cream Cheese: In another bowl, beat the softened cream cheese until smooth and creamy. Add the sweetened condensed milk, fresh lime juice, lime zest, and vanilla extract. Continue mixing until everything is well combined.
3. Combine the Whipped Cream and Cream Cheese Mixture: Gently fold the whipped cream into the cream cheese mixture. Be careful not to deflate the whipped cream – fold until it’s just incorporated, leaving the mixture light and airy.

Assemble the Cake

1. Layer the Graham Crackers: In an 8×8-inch or 9×9-inch square baking dish (or a similar-sized rectangular dish), lay down a layer of graham crackers, covering the bottom completely. You may need to break some crackers into smaller pieces to fit the shape.
2. Spread the Filling: Spoon about one-third of the lime mixture over the graham crackers, smoothing it out with a spatula. Repeat the process with additional layers of graham crackers and lime filling until you have three layers of graham crackers and two layers of the lime filling.
3. Finish with the Final Layer: Once the last layer of lime filling is spread on top, cover the entire dish with plastic wrap and refrigerate for at least 4 hours, or preferably overnight. This will allow the graham crackers to soften and absorb the filling, creating that signature icebox cake texture.