For the sauce: In a medium bowl, toss the bread with enough water to really moisten it up; you want it almost soggy. Then squeeze out the excess water, and place the bread, vinegar and garlic in a food processor and puree until smooth. While the machine is still running, drizzle in the olive oil and process until combined. Add the chives and parsley, and pulse a few more times to combine. Season with salt and more vinegar, if you like (I like a very bright, acidic dipping sauce). Transfer the sauce to a serving bowl.
For the cauliflower: Bring a large pot of well-salted water to a boil. Fill a large bowl of well-salted water with ice, and line a baking sheet with paper towels.
Toss the cauliflower in the boiling water. When the water returns to a boil, cook the cauliflower for 2 more minutes, then drain and immediately plunge the cauliflower in the ice water. When the cauliflower is cool, drain and lay it out to dry on the prepared baking sheet.
In a large saucepan, pour enough peanut oil to fill the pan 1 1/2 to 2 inches up the sides. Heat over medium-high heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F. To see if it's hot enough, drop some flour into it. If the flour sizzles and floats quickly, you're good to go. If the flour burns or the oil begins to smoke, it's too hot, so reduce the heat.
Set up standard breading procedure: one bowl of the flour, one bowl for the eggs, beaten with 2 tablespoons water, and one for the breadcrumbs and Parm. Then place a couple layers of paper towels on a baking sheet next to the stovetop. When the oil is hot, dredge some cauliflower in the flour and shake off the excess, then dip it in the egg mixture, and finally through the breadcrumb mixture. Repeat this process for the remaining cauliflower.
Working in batches so you don't overcrowd the pan, fry the cauliflower until brown and crispy, 3 to 5 minutes. Transfer the cauliflower to the paper towels, sprinkle with salt, and serve hot, hot and hot with the agliata sauce.