The first time I ate pulpo gallego was in Galicia, the northwestern Spanish region from which it hails, and I wasted no time doing it. I'd gone there to work on a farm for several weeks, arriving with a list of Galician dishes I was dead set on eating while there. Also called pulpo á feira due to its popularity at parties and festivals, pulpo gallego is a small, tapas-style dish of octopus dressed with olive oil and a sprinkling of pimentón de La Vera (Spanish smoked paprika) on top.
As soon as I got to the farm, I started chatting up Vicente, one of the owners, about it, asking him to recommend a restaurant in the nearest city where I could try it. No, he told me, none of the restaurants were worth visiting. Apparently, tight fishing regulations meant that none of them could get their hands on octopus from Galician waters for much of the year, forcing them to buy it from fisheries farther afield, including in Africa and the Canary Islands.* He made it clear, in the way a prideful native of any place will, that octopus from those waters was vastly inferior to the Galician kind.
This was a decade ago, so I'm not sure whether the octopus-fishing regulations in Galicia are the same today or not.
I was crushed—I'm an octopus lover, so this was one of the Galician dishes I was most excited about tasting at its origin. But before I could mope for long, Vicente rescued my mood by adding a crucial detail: He always packed his freezer with as much Galician octopus as he could fit, buying it from a local fisherman during the brief window each year when its fishing was allowed.
The next day, he held a massive octopus above a pot of simmering water and dipped it in three times, telling me this helped set the purple skin so that it wouldn't fall off as the octopus spent the next hour in boiling water. (I have yet to verify this claim, though it seemed to work for him.) Once it was cooked, he cut the tentacles into rounds and sliced the edible parts of the head into strips, arranged the pieces in a single layer on a plate, then topped them with the oil, pimentón, and salt. That was it. It was hands down the best octopus I've ever eaten, rich with an extra-thick layer of gelatin under the skin.
Whether it was objectively superior, or just superior by virtue of the setting, I can't say, but it sure seemed perfect at the time.
Sadly, I can't get Galician octopus in New York, but I still continue to enjoy the dish at home today. There's not much to the recipe itself, given how few ingredients it involves, so the biggest change I've made to the recipe is that I usually use a pressure cooker to cook my octopus, which cuts the cooking time down from about an hour to just 25 minutes (including the time it takes to bring the cooker up to high pressure).
Here's one more pro tip I picked up from Vicente: Folks sometimes serve this dish with sautéed onions and boiled potato slices, which help stretch it into a heartier meal. If you decide to do it like that, try boiling the sliced, peeled potatoes in the octopus cooking water after the octopus has come out. They'll absorb the octopus flavor, so that even the starchy bites deliver that same great Galician taste, no matter where you are.