For the octopus:
Preheat oven to 225°. Put all confit ingredients together in an oven- proof pot that’s not too large. You want the octopus to fit snugly. Cook in oven at 225° for 1½ hours or until knife-tender. When tender, remove from oil and let cool.
Cut tentacles from head and marinate tentacles overnight in a mixture of fresh Italian parsley, lime zest, sliced jalapeños, and extra- virgin olive oil. They do not need to be weighted down, just tossed with marinade and stored in a covered container overnight.
For the gnocchi:
Place potatoes onto a clean work surface. Make a well in the center of the potatoes, and sprinkle all over with flour. Add the egg yolks, salt, and Parmesan. Using a bench scraper, start cutting all the ingredients together (using the biscuit theory). When all ingredients are almost formed together, gently knead for 1 minute until a ball is formed.
DO NOT OVERWORK! Let rest at room temperature for 30 minutes. After the dough has rested, bring a large pot of salted water to a boil and set up an ice bath nearby. Divide the dough into 8 balls. Roll 1 ball out at a time into a rope (¾-inch in diameter) and cut the rope into 1-inch pieces. Drop the dough pieces in boiling water in batches until they rise to the top of the water, about 1 minute.
Use a slotted spoon to transfer the gnocchi to the ice water. Drain gnocchi and transfer to a mixing bowl, toss with a little extra-virgin oil, and store, covered, in the refrigerator for up to 48 hours.
For the salad:
Combine and toss well.
In a very hot cast iron pan, sear the octopus about 2 to 3 minutes on each side so the tentacles get nice and charred. Turn down to low and add the gnocchi—you want color, but not too much crispness, they should be pretty soft. Plate gnocchi first, top with a tentacle of the octopus, and serve with the Spicy Mint Yogurt and Salad on top to finish the dish.