In a large mixing bowl, beat the heavy whipping cream with a hand mixer or stand mixer until soft peaks form.
Add 1/4 cup of the powdered sugar and the vanilla extract, then continue beating until stiff peaks form. Set aside.
In a separate bowl, beat the softened cream cheese with the remaining 1/2 cup of powdered sugar until completely smooth and aerated.
Gently fold the whipped cream into the cream cheese mixture using a spatula until no streaks remain.
Spread a thin layer of the cream mixture (about 1/2 cup) onto the bottom of a 9x13 inch baking dish to secure the crackers.
Place a single layer of graham crackers over the cream, breaking pieces to fit the edges as necessary.
Spread one-third of the remaining cream mixture over the crackers, then top with one-third of the sliced strawberries.
Repeat the layers of graham crackers, cream, and strawberries two more times, finishing with a decorative layer of strawberries on top.
Cover the dish tightly with plastic wrap and refrigerate for at least 4 hours, preferably overnight, to allow the crackers to absorb moisture and soften into a cake consistency.