Heat the oven. Heat the oven to 160°C (320°F). Tear off a large sheet of foil and a sheet of parchment of the same size.
Wrap the octopus (about 10 minutes). Lay the parchment on the foil. Put the octopus in the center with the olive oil, bay leaves, oregano, garlic, and the lemon slices. Fold the parchment and foil into a tight packet with no gaps, so the steam stays inside.
Bake until tender (about 90 minutes). Set the packet on a sheet pan and bake. Open it carefully (the steam is hot) and test the thickest part of a tentacle with a fork. It is ready when the fork slides in with almost no resistance. If it still feels tough, rewrap and bake 30 minutes more, as the published recipe suggests.
Rest (15 minutes). Leave the octopus in its packet to cool a little. Letting it cool in its own liquid is a step another published recipe stresses, since removing the octopus straight from the heat can leave it gummy.
Roast the vegetables (35 to 40 minutes). Raise the oven to 200°C (400°F). On a large sheet pan, toss the potatoes, carrots, and onion with the oil, salt, and paprika, and spread them in one layer. Roast, turning once, until the potatoes have deep golden edges and the carrots are tender. The kitchen should smell sweet and toasted.
Cut and dry the octopus. Remove the head, if still attached, and cut the tentacles into 2-inch (5 cm) pieces. Discard the garlic and bay leaves. Pat the pieces very dry with paper towels. This matters, since moisture is the enemy of crispness.
Crisp (about 4 to 6 minutes). Heat the tablespoon of oil in a large skillet over high heat until it shimmers. Add 3 or 4 pieces at a time so the pan stays hot. Sear about 2 minutes per side until deep golden and crisp at the edges. Repeat with the rest.
Serve. Pile the octopus over the vegetables, squeeze over the juice of the remaining lemon half, drizzle with extra-virgin olive oil, and scatter the parsley.