1. Cook the potatoes in a saucepan of boiling salted water for about 10 minutes, or until tender. Drain, rinse with cold water, then pat dry with kitchen paper.
2. Place a large saucepan or wok over a medium heat. Add about 500ml (16fl oz) of water and bring to the boil. Add the mussels and increase the heat to high. Cover with a tight-fitting lid and cook for 3 minutes, giving the saucepan an occasional shake. Uncover and stir well. As the mussels open, remove them to a platter. Discard any that haven't opened after 5 minutes. Remove the mussels from their shells and set aside.
3. Heat the oil and butter in a large non-stick frying pan, add the garlic and shallot, and fry for about 3-4 minutes. Add the potatoes, raise the heat and sauté, shaking the pan occasionally for about 10 minutes, or until they are golden and crisp. Add the pepper, mussels and spices, and sauté for 2-3 minutes. You can pop this under a hot grill to finish off if you like it crispy.
4. Scatter with parsley and season to taste. Serve with wedges of iceberg lettuce dressed with a little mayonnaise.