Thoroughly clean all the shellfish and seafood before beginning.
Place the mussels and clams in a large skillet along with 2 tablespoons of extra virgin olive oil and the 2 garlic cloves. Cover with a lid and cook over medium-high heat for about 4 minutes until they open.
Once the mussels and clams are fully opened, remove from the heat and shell them, setting them aside. Discard any shells that did not open.
Fill a large pot with water and add the lemon cut into quarters, a sprig of parsley, and the celery stalk. Bring the water to a boil.
Once boiling, submerge the octopus. Lower the heat and let it simmer gently for about 40 minutes per 1 kg of octopus (cooking time may vary depending on size).
When the octopus is tender, remove it from the water and set aside. In the same simmering water, add the squid and cook over low heat for about 10 minutes.
Remove the squid, then drop in the peeled shrimp and cook for just 3 minutes. Remove and set aside.
Cut the cooked octopus and squid into bite-sized pieces. Finely dice the carrot and the remaining celery stalk. Blanch the diced vegetables in boiling water for about 3 minutes, then drain and set aside to cool.
In a small bowl, combine the olive oil, salt, and finely chopped parsley. Whisk vigorously until emulsified.
In a large serving bowl, combine all the prepared seafood (octopus, squid, shrimp, mussels, and clams) and the blanched vegetables. Pour over the parsley emulsion and toss gently to combine thoroughly before serving.
