“Where I grew up, on the island of Crete, sweetbreads were a snack,” Michael Psilakis, the chef at the Greek restaurant Onera, said last week. “I’d walk into my mother’s house and just reach for some sweetbreads – it was just like popcorn.”

Mr. Psilakis’s eyes lit up as he said this – he clearly loves talking about food. But while he’s received well-deserved attention for his creative Greek cooking (The New York Sun’s Paul Adams described Onera as “startlingly good” when it opened last fall), little has been written about Mr. Psilakis’s secret passion: offal. Not just sweetbreads (the pancreas or thymus gland) but also liver, kidneys, tripe, brains, heart, headcheese, tongue, eyeballs – as he ran through all the possibilities, I started to realize where the term “variety meats” comes from.

Except for the sweetbreads, none of this food appears on Onera’s regular menu. But there’s a special offal tasting menu that’s available with two days’ notice – six courses, prepared and served by Mr. Psilakis, all for about $65 a person (the price can vary a bit depending on ingredient availability and market rates). Obviously, if the very idea of eating brains makes you pucker your face in disgust, this isn’t for you. But for adventurous sorts seeking a truly unique eating experience, Mr. Psilakis’s cavalcade of organ meats should be one of the city’s most fascinating meals.

But does “fascinating” correlate with “delicious”? That’s the thing about offal: The novelty factor can often overshadow the food’s gastronomic merits, and you walk away saying, “Well, that certainly was, um, interesting.” I’d long wanted to gain a greater appreciation for these foodstuffs on their own merits, and everything I’d heard about Mr. Psilakis’s cooking led me to believe that he was the ideal tour guide. So with a broad-minded associate in tow, I ventured to Onera last week and prepared to run the gauntlet of exotic body parts. Here’s how it went.

First Course: Chilled goat-kidney salad. From my perspective, this didn’t seem like an auspicious beginning – I’ve always found kidneys to be rather mealy, and I had quietly hoped that the restaurant’s supplier would be out of them. Turns out I needn’t have worried, because these kidneys, slivered small enough to make their texture more palatable, made an excellent foundation for the salad’s grilled onions, artichoke, and parsley. The masterstroke, though, was the salad’s surrounding moat of foamed avgolemono, the classic Greek egg-lemon soup – a clever nod to Mr. Psilakis’s Hellenic roots. The foam’s citrus-borne acidity let it function as a de facto vinaigrette, which played perfectly off of the robust-flavored kidney. So far, so good.

Second Course: Calf sweetbreads. This was the high point – popcorn, indeed! The sumptuous thymus glands were nicely browned and accompanied by braised cauliflower, wilted spinach, capers, a brown-butter sauce, and – in a brilliantly counterintuitive move – dried cherries. It all formed an ideal backdrop to the sublimely tender meat. “I could eat a lot more of this,” said my companion, looking at my plate with an alarmingly covetous eye. “Me, too,” I said, pulling my plate a bit closer.

Third Course: Calf brains. “Brains are usually the toughest sell,” Mr. Psilakis said as he put a plate of gray matter in front of each of us. “They’re so soft, almost like a mousse – people have trouble with the texture. But we sear it to brown the exterior a bit and top it with some crispy shallots to give it a bit of an outer crunch. See what you think.” After that buildup, I was surprised to find the brains rather unremarkable – exceedingly tender, yes, but also extremely mild-flavored, sort of like a very soft-fleshed fish. Not objectionable, but not particularly exciting either.

Fourth Course: Heliopites with seared lamb’s liver and chicken liver sauce. This small pasta course was a good transition after the creamy brains, although the finely minced liver couldn’t compete with the excellent topping of sheep’s milk creme fraiche and aged balsamic vinegar. “This seems a bit like cheating,” my sidekick said. “Okay, so it’s got liver in it, but it’s not a liver course, y’know?” I agreed, but the dish was too delicious to argue with.

Fifth Course: Grilled lamb heart. This was a revelation. If we hadn’t known better, it would have been easy to mistake these thin, red slices for rare, prime-grade flank steak. Topped with nothing more than a spritz of lemon and a drizzle of olive oil, it was magnificently meaty – not at all tough, as I’d thought would be the case. “There’s a lot of waste to a heart,” Mr. Psilakis explained. “You have to remove the outer layer of fat, and the valves – we use only the best part.” He ended up giving us a fairly detailed lesson in cardio-butchery and also enthusiastically described his recent experience of eating a tuna heart, but I was too focused on my plate to get all the details.

Sixth Course: Braised calf tongue. As the son of a good Jewish mother, I ate my share of tongue growing up. But it was never like this: thinly sliced and stewed in a magnificent ragu of porcini mushrooms and white beans, all capped by a poached egg sitting on top. “If you poke the egg, the yolk will run into the sauce – that’s the idea,” Mr. Psilakis said. We did as instructed, with spectacular results. My only gripe: This hearty, homespun course was a bit too heavy for summer, especially at the end of a long meal.

So there you are: Interesting for sure, even educational, but also sumptuous and satisfying. And thanks to the modest portions and the meal’s leisurely pace (the six courses took about two and a half hours), we even had room for dessert. No organ meats here, although the Greek yogurt with fruit and clove honey ($7) and the chocolate-and-halva truffle with toasted-sesame ice cream ($8) were as wonderful as any of Mr. Psilakis’s organ meats.

As the waiter cleared our table, I couldn’t help but feel a bit sorry for the restaurant’s other customers, who were ordering from Onera’s regular menu and had no idea of what they were missing. That’s a shame – food this good deserves more attention, no matter what part of the animal it comes from. Put aside your preconceptions and go see for yourself.

Onera, 222 W. 79th St., 212-873-0200.