How to Make It
In a large glass bowl, combine the water with the vinegar, sugar and salt; stir to dissolve the sugar and salt. Add the carrots, shallots, fennel and cauliflower, submerging them completely in the brine. Cover and refrigerate the vegetables for 24 hours.
In a medium saucepan of boiling water, cook the green beans until bright green and barely tender, about 3 minutes. Drain and refresh under cold running water. Pat the beans dry.
Drain the pickled vegetables and place in a large bowl. Add the green beans and the Bagna Cauda Vinaigrette and toss well. Arrange the vegetables on plates, top with the marinated anchovy fillets and a sprinkling of freshly ground pepper and serve.