Place 2 cups semi-sweet chocolate chips in a heatproof bowl. Heat 2/3 cup heavy whipping cream in the microwave until steaming (about 45 seconds). Pour the hot cream over the chocolate chips, let sit 1 minute, then whisk until smooth to make the ganache. Set the ganache aside to cool until slightly thickened.
In the bowl of a stand mixer or with a hand mixer, combine 3 1/2 cups heavy whipping cream, 1/2 cup powdered sugar, and 1 teaspoon vanilla extract. Whip until medium peaks form.
Spread a thin, even layer of the whipped cream across the bottom of a 9x13-inch pan.
After spreading the thin base layer, divide the remaining whipped cream into three equal portions. Also divide the cooled ganache into three equal portions.
Arrange a single layer of chocolate graham crackers over the whipped-cream-lined bottom of the pan, breaking crackers as needed to cover the surface evenly.
Spread one third of the ganache evenly over the cracker layer. Then spread one third of the remaining whipped cream evenly over the ganache.
Repeat the layering two more times: a layer of graham crackers, one third of the ganache, and one third of the remaining whipped cream. You should have three cracker layers total.
Cover the pan with plastic wrap and chill in the refrigerator for at least 4 hours, or overnight, before serving.