Line a 9×13-inch pan with a parchment sling for easy lifting. Count out about 27 graham cracker sheets and set aside; break a few to patch gaps if needed.
Make the chocolate topping first so it can cool: Place chopped chocolate, butter, and a pinch of salt in a medium heatproof bowl. Microwave the cream until steaming (45–60 seconds), then pour over the chocolate. Let sit 2 minutes, then stir from the center outward until smooth and glossy. Set aside at room temperature 25–30 minutes to thicken to a spreadable consistency.
Whisk the pudding mixes with the cold milk for about 1 minute until smooth. Refrigerate for 5 minutes to lightly set.
In a separate bowl, whip the cold heavy cream with the powdered sugar on medium-high speed until medium peaks form—creamy and billowy, not stiff (about 2–3 minutes).
Stir the vanilla extract into the chilled pudding. Fold in the whipped cream in two additions with a spatula until no streaks remain; avoid overmixing to keep it airy.
Assembly—Layer 1: Swipe a spoonful of filling over the bottom of the pan to anchor. Arrange a tight, even layer of graham crackers on top, patching corners as needed.
Spread half of the vanilla cream over the crackers all the way to the edges. Tap the pan gently to settle the layer, then add a second even layer of crackers.
Add the remaining vanilla cream, smooth, and finish with a final cracker layer, pressing lightly so everything makes contact. Cover and refrigerate 30 minutes to firm before topping.
Top with chocolate: If the ganache has thickened to a pourable-but-spreadable state, spoon it over the surface and smooth with an offset spatula. If it seems too thick, warm it in 5-second microwave bursts, stirring between each, until fluid.
Cover the pan and chill at least 6 hours, preferably overnight, so the crackers soften into cake-like layers. Slice with a knife warmed under hot water and wiped dry between cuts.