tl;dr—Book of Vile Darkness’s absorb strength allows a caster to eat a corpse and gain Constitution (and Strength); increasing Constitution grants more hp and max hp, so it’s kind of like healing, albeit only temporarily. Nothing else I’ve found really fits the bill.
Bizarrely, there are not a lot of options along these lines, not even among monsters oddly enough. I suspect there was a certain amount of “well if the PCs are dead it doesn’t really matter what the monsters do” going on there, but it does limit us somewhat. The best answer so far, by my estimation—HeyICanChan’s suggestion of the Voracious feat—is still only licensed work, not Wizards of the Coast material.
I can’t offer any better, but since I spent a lot of time looking through material for even these meager suggestions, it seemed silly not to post them:
Book of Vile Darkness has “corrupt spells,” which any spellcaster can prepare (yes, prepare—you can’t get them if you don’t prepare your spells, though the Arcane Preparation feat can help). They all deal ability score damage to the caster after they have completed, and they are all tagged with the evil descriptor. Since none of them heal you, and then they all wind up dealing ability damage to you, they really don’t apply, but several of them do involve eating foes.
- absorb mind—2nd-level divination—Caster gains a 25% chance of knowing information in a brain eaten.
- absorb strength—4th-level necromancy—Caster gains ¼ of a creature’s Str and Con when they eat it. Gaining Con increases one’s hp as well as max hp, but it only lasts 10 minutes/level. Still, probably the best option for this Wizards of the Coast published.
- consume likeness—6th-level necromancy—Caster steals the appearance of a creature, gaining a +10 bonus on Disguise checks, by eating their corpse.
Book of Vile Darkness also has the lifedrinker prestige class for vampires, as well as the soul eater prestige class, which allow healing and more from drinking blood or eating souls, respectively, but both must be inflicted on the living.
The first thing I thought of was to look into monsters that can do this, and then use shapechanging magic to turn into one. Since that ability is likely a supernatural one, you would need some ability to get supernatural features while polymorphed—either use powerful magic like shapechange, or take a feat like Assume Supernatural Ability from Savage Species or Metamorphic Transfer from Expanded Psionics Handbook (or the SRD since the feat is open-game content). For class, druid, wizard, and psion are probably the most likely candidates here, though monk or ranger could work through variants that get wild shape (Dragon vol. #324 and Unearthed Arcana/SRD, respectively). The master of many forms prestige class from Complete Adventurer will likely be important for opening up other creature types, since an ability like this is most likely found among things like aberrations and outsiders. Anyway, normally polymorphing, particularly polymorphs that include supernatural abilities, are some of the quickest ways to break the game, but limiting yourself to one particular form that has the feature you want does help a lot with reigning it back in, particularly since you aren’t going for an especially-problematic form.
Unfortunately, I cannot actually find any candidates here: the barghest kind of does it (gaining HD causes you to gain hp, after all), and the dusk giant from Heroes of Horror has a similar feature, but while gaining HD will increase your hp, it’s not really the same thing. An intellect devourer can eat the brain of a corpse (or soon-to-be-corpse) to take over that body; again, no healing. Tsochari from Lords of Madness can also pull that trick, and don’t even have to kill the target if they don’t want to—and they get to steal the target’s spell slots in the process. Still no healing.
The illithid savant prestige class from Lords of Madness can do even better if you turn into an illithid—eating brains allows the savant to steal all kinds of abilities and knowledge—but it doesn’t grant actual healing as requested. It’s also one of the most broken classes in the game, so I recommend against it.
Finally, there is swallow whole—a lot of monsters do have that. Swallow whole is a combat maneuver, though, and while it’s pretty effective at killing things, it doesn’t directly heal you. It also doesn’t let you do anything special with creatures you have already killed. But if you’re interested in it, in addition to polymorph effects to turn into something that can do it, there is also the 8th-level hunger domain spell bite of the king, found in Libris Mortis and Spell Compendium, which allows you to swallow creatures whole without having to change form.
Actually, I take back what I said about aberrations and outsiders being the most likely sources of such abilities: the undead are the ones most likely to have such a feature, but it’s likely to be obligatory, unlikely to be playable, and turning into an undead creature temporarily can be difficult. Of core spells, only shapechange can do it, and that’s a 9th-level spell. It’s hard to design a character around something you won’t have until 17th level, at best.
Libris Mortis does have a few playable undead “monster classes”—ghoul, mohrg, mummy, vampire spawn, wight, and necropolitan—but only the vampire spawn has anything close, from its blood drain ability. Again, like death knell, that only works on living targets, rather than already-dead ones (though it does not require they be dying), and grants temporary hit points, not true healing. And really, while playing a vampire spawn, or vampire, is legal under the rules, as a practical matter they are saddled with so many drawbacks in the name of balance that they actually become basically unplayable. The necropolitan is playable—it’s LA +0—but it doesn’t get any particular features aside from the undead type, nothing relevant here.
Incredibly, even ignoring the difficulty of actually managing to play some random undead, even looking at the ones I don’t think could be playable, I still cannot find any undead creatures that actually heal from eating corpses. I’m kind of flabbergasted by it, to be honest.