1. In a large mixing bowl, beat the softened cream cheese until completely smooth and creamy.

2. Add the sweetened condensed milk and mix until fully combined.

3. Pour in the fresh lemon juice, lemon zest, and vanilla extract, then beat until the mixture is silky and slightly thickened.

4. In a separate chilled bowl, whip the cold heavy cream until soft peaks form.

5. Gently fold the whipped cream into the lemon mixture until light, fluffy, and fully incorporated.

6. Spread a thin layer of the lemon cream mixture into the bottom of a 9 x 13 inch (23 x 33 cm) dish.

7. Arrange a single layer of graham crackers over the cream, breaking pieces as needed to fit.

8. Spread about one-third of the remaining lemon cream over the graham crackers.

9. Repeat the layers of graham crackers and lemon cream until all ingredients are used, finishing with a smooth layer of lemon cream on top.

10. Cover the dish and refrigerate for at least 6 hours, preferably overnight, until the crackers soften and the cake is fully set.

11. Garnish with extra lemon zest and lemon slices if desired.

12. Slice and serve chilled.