Both the Dungeon Master’s Guide and the Epic Level Handbook provide rules for continuing to gain class levels—which come with HD—indefinitely so long as you continue to accrue XP. So that is one trivial answer.
There is also an “energy charge” supernatural ability defined in Monster Manual III to grant positive levels, analogous to energy drain granting negative levels. You can also find it defined in the online glossary. No creature in the game has ever been published that actually has this ability, but RAW, manipulate form doesn’t actually care. Since we’re discussing Pun-pun, manipulate form abuse is in our wheelhouse, but even by those standards this is extreme cheese.
Granting oneself the feed ability of a barghest, and using epic magic to produce ever-greater-HD humanoids to eat, should also work. I leave whether this is greater or lesser cheese as an exercise to the reader.
Becoming an animal, casting awaken on yourself, and then becoming an animal again so you can cast awaken on yourself also should work in the kind of “no one will ever put an arbitrary end to this” game where Pun-pun is possible in the first place.
The objections to each of these in the linked article are largely specious, rely on debunking a single (not particularly detailed or thorough) Pun-pun write-up, or simply lack detail to even say what the objection is or is based on. In particular, the limitless HD section talks a lot about “actual” HD or “effective” HD, which isn’t a real game term, and on limits the author assumes to be in place that are not actually found in the relevant rules. Nothing in awaken specifies that an intelligent animal is not a valid target, or that the spell can only be used once on a given creature. Those are totally plausible limitations to enforce on it, but officially the rules rely on the type change to manage things—which Pun-pun gets around. There are repeated claims that epic options are unavailable due to the lack of 21 “actual” HD level, but Dragonwrought (or any other method of according the Dragon type) gets around that thanks to Draconomicon saying Old or older dragons can take epic feats without necessarily having 21 HD (the controversy over whether or not Dragonwrought kobolds are true dragons is irrelevant here, by the way). So that discussion—which appears to have been removed from the article itself and shoved into the talk page on the basis that the author does not have the expertise he claims—is of really limited value.