In a medium saucepan cover the potatoes with cold water. Add salt and bring to a boil. Cook until tender, about 15 minutes. Drain.
Bring a saucepan of salted water to a boil. Add the rapini 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 frypan. Cook over high heat, mashing the anchovies, for about 1 minute. Spread the mussels in the frypan, top with the potatoes, rapini and chopped parsley. Add 1/2 cup (125ml) water and season with salt. Cover and cook until mussels are open. Serve.