Place instant vanilla pudding mix and milk into a large bowl. Using a mixer or whisk, mix well to combine. Fold in the thawed whipped topping.
Cover the bottom of a 9X13 inch baking dish with graham crackers. Break them as necessary to completely cover the bottom. Each layer should use about 1 sleeve of graham crackers. Spread half of the pudding mixture evenly over this layer of graham crackers.
Use another sleeve of graham crackers to create a second layer. Spread the remaining pudding mixture evenly over this layer of graham crackers. Use the last sleeve of graham crackers to cover the pudding mixture.
Place chocolate chips, heavy cream, corn syrup, and vanilla into a medium sized microwave-safe bowl. Microwave for 1 minute, then stir. Continue cooking for 30 seconds at a time, stirring after each interval. Once you are able to stir it to a smooth consistency, allow to cool for a few minutes. After cooling slightly pour the chocolate mixture over the eclair cake. Smooth chocolate with a spatula.
Cover the cake with foil or plastic wrap and place it in the refrigerator. Chill for at least 8 hours, though overnight is prefered.