Pour the chicken broth into a large saucepan and bring it to a simmer. Peel and large dice the potatoes, add to broth and cook, covered, until they are very tender, 20 to 25 minutes.
While the potatoes cook, wash and drain the arugula. Add it to the saucepan. Stir to combine and simmer until the arugula is completely wilted, 1 to 2 minutes.
Puree with an immersion blender right in the saucepan, or in a food processor in one or two batches, transferring each batch to a clean saucepan or warm tureen. Stir in the pepper and swirl in the creme fraiche or olive oil.