Prepare Whipped Cream: In a cold bowl, whisk 1½ cups heavy cream, 3 tablespoons sugar, and 1 teaspoon vanilla extract until soft peaks form. Reduce speed to medium peaks.
Mix Pudding: In a separate bowl, whisk 2 packages of instant vanilla pudding mix with 3 cups of cold milk for 2–3 minutes until thickened. Gently fold in half of the whipped cream.
Layer the Cake: In a 9×13-inch pan, spread a thin layer of pudding mixture to coat the bottom. Press one sleeve of graham crackers into the pan, breaking as needed. Spoon half the remaining pudding over the crackers, followed by a second layer of crackers and the remaining pudding. Finish with a final layer of graham crackers.
Melt Chocolate: Heat 1 cup of heavy cream in a small saucepan until just boiling. Pour over chopped chocolate in a heatproof bowl. Let sit for 1 minute, then stir until smooth.
Apply Chocolate Layer: Spread melted chocolate over the graham cracker topping using a silicone spatula. Smooth the surface and chill for at least 2 hours or overnight.
Serve: Refrigerate for 30 minutes before cutting into 12 squares.