Cut the potatoes into large dice and combine in a large saucepan with just enough water to cover. Bring to a rapid simmer, then lower the heat, cover, and cook until the potatoes are just tender, about 10 to 15 minutes. Drain well in a colander.
Trimmed the bottom of the fennel, then trim away the stalks. Discard the stalks (or reserve them for another use, such as flavoring soup and stew bases). Quarter and thinly slice the bulb. Reserve about ¼ cup of the feathery leaves.
Combine the cooked potatoes with the sliced fennel in a serving container.
Place the ingredients for the sauce in a food processor and process until the mixture is fairly smooth, but you can leave some texture to it.
Pour the dressing over the potato mixture and toss together. Season with salt and pepper. Serve warm or at room temperature.