In a large mixing bowl, whip the heavy cream, powdered sugar, and vanilla extract together until stiff peaks form.
In a separate bowl, combine the Greek yogurt and lemon zest.
Gently fold the yogurt mixture into the whipped cream until well combined.
Line an 8x8-inch baking dish with a layer of graham crackers, breaking them as needed to fit.
Spread a layer of the whipped cream mixture over the graham crackers, then add a layer of mixed berries.
Repeat the layers until all ingredients are used, finishing with a layer of the whipped cream mixture on top.
Cover the dish with plastic wrap and refrigerate for at least 4 hours, or overnight for best results.
Before serving, garnish with additional berries and a dusting of powdered sugar if desired.
Slice into squares and enjoy!