Step 1

In a large bowl, whip 2 cups of the heavy whipping cream with ⅓ cup of the sweetened condensed milk using a hand mixer on high speed, beating until firm peaks form. In another large bowl, whisk together the pudding mix, 3 cups of cold heavy whipping cream, vanilla bean paste, and the remaining sweetened condensed milk. Fold the whipped cream into the pudding mixture in 3 additions.

Step 2

In a 13x9-inch glass baking dish, place a layer of graham crackers, breaking up crackers as needed to fill any gaps. Spread half of the pudding mixture in an even layer on top of the graham crackers. Add another layer of graham crackers. Top with the remaining pudding mixture. Top with a final layer of graham crackers, cover, and refrigerate until chilled, 30 minutes.

Step 3

Place the chopped chocolate in a medium heatproof bowl. In a large glass measuring cup or another medium heatproof bowl, microwave the remaining 1 cup of heavy cream until steaming, 45 seconds to 1 minute. Immediately pour the warm cream over the chocolate and allow to sit for 1 minute before whisking until smooth.

Step 4

Pour the ganache over the chilled cake, smoothing with a spatula. Using a spoon, create a swooping effect in the chocolate, if desired. Cover and refrigerate until chilled and set, at least 4 hours or overnight.