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1
Bring a large, uncovered pot of water to a full rolling boil. Take the thawed octopus by the head and submerge it completely in the boiling water for ten seconds, then lift it clear. Repeat twice more, for three dips in total. On the third dip, lower the octopus fully into the pot and leave it there. The skin will have visibly set and taken on a uniform deep-violet colour.
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2
Maintain the water at a rolling boil — uncovered throughout — so the circulating water agitates the octopus gently and prevents uneven hot spots. Cook for approximately 45–55 minutes depending on size. This is where the dish lives or dies: at intervals from 40 minutes onward, insert a toothpick into the thickest part of an arm. When it slides in with minimal resistance — neither catching on rubber nor sinking into woolly softness — the octopus is done.
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3
Remove the pot from the heat. Leave the octopus submerged in the cooking liquid, uncovered, for 20 minutes. The residual heat will penetrate evenly and complete the tenderising. The arms will lie fully relaxed and the liquid will have quieted to stillness.
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4
Lift the octopus onto a board and slice the arms into rounds no thicker than 1 cm, arranging them directly onto a wooden serving board as you cut. As each slice falls, drizzle a first pass of olive oil over the cut surfaces so it is absorbed immediately. The oil should be liquid on contact; if it pools and congeals, the octopus is too cold.
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5
Season with coarse sea salt, dust evenly with pimentón de la Vera, and make a second pass of olive oil immediately before carrying the board to the table. The oil should pool visibly between the slices and carry the paprika across every piece. The aroma at the table should be of warm smoke and sea salt.