Cut the fronds from the fennel bulbs and reserve some of the feathery leaves for later.
Cut each fennel bulb in half and remove the cores with a sharp knife. With a mandoline slicer, cut the fennel into paper thin slices. You can also do this in your food food processor using the thinnest slicing blade. Cut the fennel bulbs into wedges and place horizontally into the feed tube. Process in batches.
Peel each orange, remove the pith with a knife, and slice. Set aside.
For the dressing: Whisk together the oil, juice, 1 teaspoon salt and the pepper in a small bowl.
Place the fennel slices, oranges slices in a large bowl. Toss with the arugula. Pour the dressing over the salad and toss together.
Sprinkle with salt and add some fennel fronds for decoration.