Hull and slice 1½ pounds of strawberries. Toss with 2 tablespoons granulated sugar and set aside for 10 minutes so they release a little juice.
In a large bowl, beat the softened cream cheese until smooth. Add the heavy cream, powdered sugar, and vanilla. Whip on medium-high speed until stiff peaks form. The mixture should look thick and hold its shape.
Spread a thin layer of the cream mixture on the bottom of a 9×13-inch dish. This helps the crackers stick. Arrange a single layer of graham crackers on top, breaking pieces as needed to fit.
Spread about one-third of the remaining cream over the crackers. Spoon half of the sugared strawberries (and their juices) evenly over the cream.
Add another layer of graham crackers, then more cream, then the remaining strawberries. Finish with a final layer of crackers and the rest of the cream. Smooth the top.
Cover tightly with plastic wrap and refrigerate for at least 4 hours, preferably overnight. The crackers will soften into tender layers.
Just before serving, top with extra sliced strawberries and a few mint leaves if desired. Slice into squares and serve cold.