On two large sheet pans, divide bell peppers, zucchini and eggplant. Drizzle the contents of each sheet pan with 1/4 cup olive oil. Season with salt and black pepper, and toss to evenly coat. In batches, grill the vegetables, turning occasionally, until cut sides are tender and lightly charred, 3 to 5 minutes for the lettuce, 8 to 10 minutes for the zucchini, and 10 to 12 minutes for the peppers and eggplant. Transfer them to one very large (or two large) serving platters as they finish cooking.
Step 3
Meanwhile, in a medium bowl, combine lemon juice, anchovies and garlic; whisk until well blended. And salami, cherry peppers, olives, celery, parsley and the remaining 3/4 cup oil, and mix well. (Makes about 2 cups neonata.)
Step 4
Generously drizzle or spoon some of the neonata over the grilled vegetables. Serve vegetables warm or at room temperature, with the remaining neonata on the side.