Bring a small saucepan of water to a boil. Reduce the heat to low and add the desalted cod, immersing it completely. Let it cook for about 3 minutes, until it flakes easily with a fork. Remove with a slotted spoon and let drain on a paper towel-lined plate. Let cool completely, then gently flake it apart.
To make the dressing, place half of the pomegranate arils in a blender with the olive oil and orange juice. Blend until emulsified, then strain through a fine-mesh sieve and set aside.
Peel the orange and remove all the white pith. Cut the fruit crosswise into thin slices.
Arrange the salad in a serving dish for the center of the table. Fill the base of the dish with dressing; pour the remaining dressing into a sauceboat to serve on the side.
Arrange the orange slices over the dressing, followed by the cod, onions and olives (this part is so soothing to me!). Finely grate the egg yolk over the salad, then sprinkle with the remaining pomegranate arils. Drizzle with extra-virgin olive oil.
I find that the salt cod and olives add enough salt, but try a bite with all of the ingredients together to see if more salt is needed.
Right before serving, spritz the salad lightly with orange flower water—a little goes a long way.