Prepare the calamari: Rinse the bodies and set aside. Dice the tentacles and the shrimp into 1/4-to-1/2-inch pieces. Beat the egg in a large bowl. Add the diced calamari tentacles and shrimp, the breadcrumbs, cheese, parsley, basil, lemon zest and juice, anchovies and garlic. Add 3 tablespoons olive oil, 3/4 teaspoon salt, and pepper to taste and mix until combined.
Using your fingers, stuff each calamari body about two-thirds full with the shrimp-breadcrumb mixture and close with a toothpick. Heat the remaining 3 tablespoons olive oil in a wide pot over medium-high heat. Sear the calamari in batches until browned and opaque on both sides, 8 to 10 minutes, and transfer to a plate.
Make the sauce: Lower the heat, add the garlic and red pepper flakes to the pot and cook, stirring, 1 to 2 minutes. Season with salt, then add the wine and scrape up any browned bits from the pot. Boil until the wine is almost evaporated, then crush the tomatoes into the pot with your hands and add the juices. Add 1 cup water, 3/4 teaspoon salt and the basil stalks. Arrange the calamari in a single layer in the pot. Bring to a simmer, cover and cook until the calamari are tender, about 40 minutes. Uncover and cook until the sauce thickens, 10 to 15 more minutes.
Meanwhile, make the polenta: Place 4 1/2 cups cold water in a separate pot over low heat. Add 2 tablespoons olive oil, 1 teaspoon salt and the bay leaf. Whisk in the polenta in a slow, steady stream, then increase the heat to medium and bring to a boil, whisking frequently. Reduce the heat and cook at a bare simmer, stirring with a wooden spoon, until the polenta is thick and pulls away from the sides of the pot, about 25 minutes. Remove from the heat and stir in the butter and cheese.
Divide the polenta among shallow bowls. Discard the toothpicks and place the calamari on top of the polenta. Remove the basil stalks and spoon the sauce over the dish. Garnish with the chopped basil and more parmesan.