Line a 9x13-inch metal baking pan with parchment paper. Leave a 2-inch overhang on the long sides.

Place a solid layer of graham crackers at the bottom of the pan. Break some crackers to fill any small gaps so the ice cream base cannot seep underneath.

In a large bowl or with a stand mixer fitted with the whisk attachment, beat the cold heavy whipping cream on medium-high speed until stiff peaks form. Do not over-beat until it becomes grainy.

In a separate large bowl, whisk together the chilled sweetened condensed milk, vanilla bean paste, and salt. Gently fold about a third of the whipped cream into the milk to lighten it. Then, fold in the remaining whipped cream until no white streaks remain.

Layer 1: Pour half of the ice cream mixture over the bottom crackers. Spread it into an even layer with an offset spatula.

Layer 2: Add a second layer of graham crackers directly on top of the cream.

Layer 3: Pour the remaining ice cream mixture over the second cracker layer and smooth it out.

Layer 4: Add the final layer of graham crackers.

In a microwave-safe bowl, combine the chocolate chips, heavy cream, and corn syrup. Microwave in 30-second intervals, stirring in between, until completely smooth. Stir in the vanilla extract. Let the ganache sit for 5 minutes to cool slightly so it does not melt the top layer of cream.

Pour the warm ganache over the top layer of crackers. Spread it to the very edges.

Place the pan flat in the freezer. Freeze for at least 8 hours, though overnight is preferred. This ensures the crackers soften just enough to become "cake-like" while the ice cream fully sets.

Sprinkle a few extra graham cracker crumbs or a tiny pinch of flaky sea salt over the ganache before it fully freezes (optional).

Once frozen, grab the parchment handles and lift the entire block onto a cutting board.

Use a sharp knife to cut the ice cream cake into slices and serve.