Prepare the fritto misto: Whisk 2 eggs, 3 cups milk and 1 teaspoon salt in a large shallow bowl. Whisk the remaining 2 eggs and 3 cups milk, and 1 teaspoon salt in another shallow bowl. Butterfly the shrimp with a small sharp knife, cutting along the curve from top to tail almost all the way through. Add the shrimp and squid to one of the bowls. Add the onion, cauliflower and sweet potato to the other bowl. Refrigerate at least 30 minutes, or until ready to fry.
Meanwhile, make the dip: Pile the anchovies, parsley and capers on a cutting board, then chop and mash them into a coarse paste. Transfer to a bowl along with the lemon juice and red pepper flakes. Gradually add the olive oil, whisking until emulsified. Refrigerate until ready to serve.
Preheat the oven to 350 degrees F. Fill a deep fryer to the fill line with half peanut oil and half olive oil; heat to 375 degrees F. Line 3 baking sheets with paper towels. Mix the flour, 1 teaspoon salt and 1/2 teaspoon pepper in a large shallow dish.
Remove the onion rings from the milk mixture and dredge in the flour. Add to the frying basket along with a slice of lemon and a rosemary sprig. Fry until crisp, about 5 minutes (cover if your fryer has a lid). Lift the basket, allowing the excess oil to drain off. Transfer the onion rings to one of the prepared baking sheets and keep warm in the oven. Repeat with the cauliflower and sweet potato, coating and frying them in batches and adding a lemon slice and rosemary sprig to each batch. (Make sure the oil reaches at least 365 degrees F between batches.) Transfer the vegetables to the prepared baking sheets and keep warm in the oven.
Coat and fry the shrimp and squid in small batches in the same manner. Sprinkle the fritto misto with salt while it's hot and transfer to a platter. Serve with the dip.