In a mixing bowl, vigorously whisk the vanilla pudding mix with the cold milk until a smooth consistency forms and the mixture begins to thicken. Gently fold in the thawed whipped topping until fully combined.
In a 9x13-inch rectangular dish, arrange a single layer of graham crackers across the base, breaking a few if needed to ensure full coverage.
Spread half of the pudding and whipped topping mixture over the graham cracker base, smoothing it evenly with a spatula.
Place another layer of graham crackers over the pudding layer, aligning them snugly.
Evenly distribute the remaining pudding mixture atop the second graham layer and smooth the surface.
Add a final layer of graham crackers to cap the dessert.
Warm the chocolate frosting slightly in the microwave (about 20 seconds), then stir until smooth. Carefully spread the softened frosting over the top graham cracker layer, covering it completely.
Cover the assembled dessert and refrigerate for at least 8 hours, or ideally overnight, to allow the layers to meld and the graham crackers to soften.
Serve chilled. Keep any remaining portions covered and stored in the refrigerator.