Bring 6 quarts of water to a boil and add 2 tablespoons salt. Plunge the cauliflower florets and leaves into the boiling water and cook 9 to 10 minutes, until tender. Remove the cauliflower, reserving the boiling water, refresh in ice water, and set aside.
Remove 2 quarts of the boiling water (to leave about 1/2 gallon) from the pot and add 3 cups white wine vinegar, salt, fennel seeds and garlic and bring to a boil. Drop the carrots, celery, cippolline and fennel into the water and vinegar solution and cook until tender, 10 to 12 minutes. Remove the vegetables and garlic. Refresh all in an ice bath and drain well.
In a large mixing bowl, place the cauliflower, cooked vegetables, garlic, anchovies, both kinds of olives and the vinegar and oil. Season with salt and pepper, toss well to mix and arrange on a platter with the olives and anchovies near the top and serve.