Sauce: In a casserole set over moderate heat, cook the onion and garlic in the oil, stirring occasionally, for 5 minutes, or until translucent. In a blender or food processor, puree the tomatoes, water, and tomato sauce until smooth and add it to the casserole. Add the carrots, potato, basil, cayenne, and salt. Bring the liquid to a boil and simmer, partially covered, stirring occasionally, for 1 hour.
Rinse the squid and turn the body sacs inside out. Mince the tentacles.
In a skillet set over moderate heat, cook the onion and garlic in the oil, stirring occasionally, for 3 minutes more.
Transfer to a bowl. Add the sea legs, eggs, bread crumbs, grated cheese, and salt and pepper.
Combine the mixture well. Stuff the squid with the bread crumb mixture and close with a toothpick. Add the squid to the sauce and simmer for 10 to 15 minutes, or until just tender. Transfer the squid to a serving dish.
Meanwhile, cook the linguini according to package directions, drain, and transfer it to a large bowl. Add enough sauce to coat the pasta and toss to combine. Sprinkle with cheese. Serve the squid separately with a mixed green salad.