Tenderize the octopus by pounding it gently, or by throwing it forcefully into your kitchen sink about 10 times.
Combine all the ingredients for the cooking liquid in a pot and bring it to a boil over high heat.
Dip the octopus in and out of the boiling liquid quickly three times, then place it in the liquid, return to the boil, and simmer covered for 1 hour.
Let the octopus cool in the cooking liquid.
Drain the octopus, reserving 1 cup (250 ml) of the cooking liquid for the sauce.
Remove and discard the skin from the octopus, cut the tentacles into 1-inch (2 cm) pieces with scissors, and discard the head of the octopus.
Heat the oil in a skillet over moderate heat and saute the octopus and garlic for 1 to 2 minutes.
Add the remaining ingredients and bring to a boil.
Simmer for 5 minutes and serve hot or at room temperature.