Add 2 tablespoons salt, peppercorns, and the wine cork; bring to a boil over high heat. Meanwhile, place octopus on a cutting board.
Using a wooden spoon or meat mallet, pound the octopus multiple times, starting in the middle and moving down each tentacle to tenderize the meat. Dip tentacles into the boiling water 3 times, holding them in the boiling water 2 to 3 seconds each time, until the tentacles curl up. Submerge entire octopus in the boiling water.
Add the penne, cheese, and a splash of the reserved cooking water to the skillet
and toss. Add more cooking water to thin the sauce, if needed. Season with salt and ground black pepper.
Bring water back to a boil, reduce heat to low, cover, and simmer until octopus is fork-tender, 45 to 60 minutes. Remove from heat and cool for 30 minutes.Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Grill octopus until charred on all sides, 3 to 4 minutes per side.