In a mixing bowl, whisk the instant vanilla pudding mix with the cold milk until completely smooth. Place it in the fridge so the pudding can set.
Add 1 cup heavy cream into a mixing bowl and add the powdered sugar. Beat it with a mixer until stiff peaks form.
Using a spatula, gently fold the whipped cream and the vanilla extract into the chilled pudding mixture until combined. Make sure to fold and not mix.
Heat the remaining 2/3 cup heavy cream in a saucepan over medium heat until it begins to simmer. Remove it from the heat.
Place the chocolate chips and butter in a heat-resistant bowl and pour the warmed heavy cream over them. Let the mixture sit for 2 minutes, and then whisk it until smooth. Stir in a pinch of salt, set aside, and let the ganache cool to room temperature.
Arrange a layer of graham crackers (or cookies) in the bottom of a 9x13-inch dish.
Spread half of the pudding mixture evenly over the graham crackers.
Add a second layer of crackers on top of the pudding, then spread the rest of the pudding evenly on top.
Add a third layer of crackers on top of the pudding.
Add the cooled chocolate ganache over the cake and spread it out evenly.
Put the chocolate eclair cake in the fridge for at least 4 hours, and up to overnight.
Slice and serve cold.