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In Greece, seaside streets are lined with octopuses, stretched from limb to limb to limb to limb, hang-drying in the sun. It's an old tenderization technique that dehydrates the octopus before it's braised and grilled. If your neighbors would tolerate it, and if you live in a similarly hot and dry Mediterranean climate, then I suppose you, too, could attempt to prepare your octopus this way—maybe you already do, since meeting those criteria means there's a good chance you already live in Greece. The rest of us aren't so lucky. No matter, grilling octopus that's crispy and tender is easy, and requires little more than a pot and a grill.
If you've never grilled octopus before, the first thing you need to know is that you can't just toss a raw octopus on the grill and call it a day. Well, you can, but I don't think you'd want to, unless the idea of rubbery, shriveled, and burnt tentacles appeals to you. Before grilling, an octopus first has to be cooked until tender. This two-stage cooking process guarantees great results.
During the first stage, your goal is to cook the octopus until the tough connective-tissue collagen in its muscles melts into soft gelatin. This takes a while because octopus is packed with cross-linked collagen, which makes it exceptionally rubbery. Its collagen-rich flesh is a direct result of its anatomy—lacking bones, an octopus evolved the structural support necessary for movement through its muscles themselves, which are known scientifically as muscular hydrostats. Thanks to their crisscrossing muscle fibers, octopus limbs are capable of complex and multi-directional movement patterns without any skeletal support. Despite our extremely distant evolutionary relationship to octopuses (they're some of our most removed animal relatives), the underlying physiology is the same as that of our tongues.
There are different ways to soften this rigid muscular flesh through cooking: sous vide uses lower temperatures and takes the longest at about five hours; simmering or boiling reduces that time to roughly one hour; and a pressure cooker can force the boiling point of water higher and speed up the cooking time to 15 minutes or so.* I've gone into more detail on these methods in my article on cooking octopus.
* Remember that octopus cooking times can vary dramatically. It's ready when it's ready and not a moment before, whether it takes 30 minutes or 5 hours.
Once cooked, you should cool the octopus down in its cooking liquid. This may sound unnecessary. After all, why bother cooling it down if you're just going to get it hot again? But I've found that octopus skin is too fragile right after boiling, rubbing off under even the most gentle touch. Some folks think removing the skin is a good thing. I don't. I love the skin and its melting texture, and I want to keep it. Chilling the octopus sets the skin, so that when it comes time it comes time to grill it, you'll be able to.
Once cooled, it helps to drain and dry the octopus. Any excess liquid on its surface will only slow down the browning and crisping you want to happen on the grill. You can pat the octopus dry with towels, or set it on parchment-lined baking sheets and allow it to air-dry in the fridge for a few hours or overnight.
Grilling is the easiest step of all. Toss the octopus, whether whole or divided into tentacles, with some olive oil and load it onto a cleaned and preheated grill, directly over hot coals. The tentacles will take on an appealing charred appearance and flavor, and the thins ends will char and get a little crispy. This grilling step is really just a surface treatment: When both sides look done, the octopus is ready. There's no need to worry about synching up outer browning and inner doneness, because you've taken care of each separately. The results: octopus that is tender, not rubbery, and lightly singed on the surface.