In a medium saucepan, cover the potatoes with cold water. Add salt and bring to the boil. Cook until tender, about 15 minutes. Drain.
Bring a saucepan of salted water to the boil. Add the broccoli rabe and cook until just tender; it should be bright green. Drain well and cut into 5cm lengths.
Combine the oil, anchovies and garlic in a large, deep frying pan. Cook over high heat, mashing the anchovies, for about 1 minute. Spread the mussels in the frying pan, top with the potatoes, broccoli rabe and chopped parsley. Add 120ml water and season with salt. Cover and cook until mussels are open. Serve.
If broccoli rabe is unavailable, use kale or Swiss chard instead.