1. Prepare the Cream Cheese Mixture: In a large mixing bowl, combine the softened cream cheese, granulated sugar, and vanilla extract. Beat with an electric mixer on medium speed until the mixture is smooth and creamy, with no lumps. Scrape down the sides of the bowl as needed to ensure everything is well incorporated.

2. Whip the Heavy Cream: In a separate, chilled bowl, pour the cold heavy cream. Using an electric mixer, beat the cream on high speed until stiff peaks form. This means the cream will hold its shape when the beaters are lifted. Be careful not to overbeat, or it will turn grainy.

3. Combine the Filling: Gently fold the whipped cream into the cream cheese mixture using a spatula. Do this in two additions to maintain the airiness of the whipped cream. Mix until just combined and no streaks of cream cheese or whipped cream remain. The filling should be light and fluffy.

4. Layer the Cake Base: Arrange a single layer of vanilla wafers on the bottom of a 9×13-inch baking dish. You might need to break some wafers to fit them snugly and cover as much of the bottom as possible. This forms the sturdy base of your cake.

5. Add Filling and Strawberries: Spread about one-third of the cream cheese filling evenly over the layer of vanilla wafers. Then, arrange a layer of sliced strawberries over the filling. Try to cover the entire surface with strawberries for a beautiful presentation and balanced flavor.

6. Repeat the Layers: Continue layering with another single layer of vanilla wafers, followed by another third of the cream cheese filling, and then another layer of sliced strawberries. Repeat this one more time, ending with a final layer of vanilla wafers on top.

7. Chill Thoroughly: Cover the baking dish tightly with plastic wrap. Place the icebox cake in the refrigerator and chill for at least 4 hours, or preferably overnight. Chilling is crucial for the wafers to soften and absorb the creamy filling, creating that signature cake-like texture.

8. Garnish and Serve: Before serving, you can garnish the top with a few fresh strawberry slices or a sprinkle of finely crushed vanilla wafers for extra visual appeal. Slice and serve cold.