Rinse the strawberries under cool water and pat them completely dry with a paper towel. Hull and thinly slice the strawberries, setting aside a few whole berries for the garnish.
In a large mixing bowl, combine the heavy cream, powdered sugar, and vanilla extract. Use an electric hand mixer on medium-high speed to beat the mixture until stiff peaks form, about 3 to 4 minutes.
Spread a very thin layer of the whipped cream on the bottom of a 9x13 inch baking dish to prevent the crackers from sliding. Arrange a single layer of graham crackers in the dish, breaking some crackers as needed to fill in any gaps.
Spoon and spread about one-third of the whipped cream evenly over the graham cracker layer. Arrange half of the sliced strawberries in a single layer over the whipped cream.
Repeat the layering process: add another layer of graham crackers, followed by another third of the whipped cream and the remaining sliced strawberries.
Finish with a final layer of graham crackers and spread the remaining whipped cream over the top. Decorate the top with the reserved whole strawberries and mint sprigs.
Cover the baking dish tightly with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, until the graham crackers have softened to a cake-like texture.