I take a double pun to mean a pun that hurts twice - once when you get it, and again when it's explained how you didn't actually get it after all. Lest I bother to try to explain this indirectly, let me simply proceed to my meager set of examples.
The story goes that Voltaire was visiting Frederick the Great, and they went out one morning to hunt, with each man hiding in a separate spot to watch for game. As noon approached, Frederick, who generally spoke in French, sent a servant with a message to Voltaire, asking if he was hungry yet. Voltaire's note came back with the simple word "Ja!". As they rode back to the palace together, Frederick said jokingly, "But Voltaire, when did you condescend to learn German?" and Voltaire replied, "I do not know what you mean, sire. My response is simple to read: 'J grand A petite'". Here, when spelled out, the phrase can be read as "Jai grand appetit", that is, "I have a great appetite".
Ekkehard Sachs is a mathematics professor with a special interest in computational optimization. So it is little surprise that his license plate reads "1TR8", that is, "iterate", describing the common technique of repeated application of an improvement process in order to reach an optimal solution to a problem. If you tell him you've figured out his license plate, though, he will laugh and say, "But don't you realize I'm a big fan of the German soccer team Eintracht?" And of course, "1TR8" = "Ein+TR+Acht" = "Eintracht" as well!