In a large bowl, whisk the instant pudding mixes with the cold milk for about 2 minutes, until thickened.
Whisk in the vanilla extract.
Fold in the whipped topping until smooth and fluffy.
Place a single layer of graham crackers in the bottom of a 9×13-inch baking dish, breaking crackers as needed to fit.
Spread one-third of the filling over the crackers.
Add another layer of graham crackers, then another one-third of the filling.
Add a third layer of graham crackers, then the final one-third of the filling. Top with a final layer of graham crackers.
Microwave the chocolate frosting for 10 to 15 seconds. Stir, then add 2 tablespoons milk and stir again. Add 1 more tablespoon milk if needed for a smooth, spreadable consistency.
Spread the softened frosting evenly over the top cracker layer.
Cover and refrigerate at least 8 hours, preferably overnight. Slice and serve cold.