In a mixing bowl, combine the sliced strawberries with granulated sugar. Stir well to coat the strawberries evenly, and let the mixture sit for approximately 15 minutes.
While the strawberries sit, in a separate mixing bowl, whip the heavy cream along with powdered sugar and vanilla extract using an electric mixer. Beat until the mixture reaches stiff peaks. Carefully fold in the fresh lemon zest.
Begin assembling the cake in a large serving dish or a rectangular cake pan. Start by spreading a thin layer of the whipped cream mixture evenly across the bottom of the dish.
Layer graham crackers on top of the whipped cream, ensuring they cover the entire base of the dish completely.
Spoon a generous portion of the prepared sugared strawberries over the graham crackers, making sure to spread them out evenly.
Add another layer of whipped cream over the strawberries, smoothing it out with a spatula.
Repeat the layering process with graham crackers, followed by strawberries, and then whipped cream, until you have utilized all of your ingredients.
Cover the assembled icebox cake tightly with plastic wrap and refrigerate it for a minimum of 4 hours, or preferably overnight.
Just before serving, garnish the top of the cake with additional fresh strawberries and a sprinkle of mint leaves.
Notes
For best results, refrigerate overnight to allow flavors to meld.