Melt the butter in a large saucepan over a medium-low heat and cook the shallots and 2 of the garlic cloves for 5–6 minutes, until softened. Pour in the wine, increase the heat slightly and bring to the boil.
Tip the mussels into the pan, discarding any that won’t close when sharply tapped, then cover and simmer gently for 3–5 minutes, shaking the pan occasionally, until the shells are opened. Discard any that remain closed. Set aside until cool enough to handle.
Meanwhile, put the breadcrumbs in a bowl with the parsley, remaining garlic, lemon rind, Parmesan and oil and mix well.
Discard the empty half-shell from each mussel and arrange the mussels in a single layer on a large baking sheet.
Spoon the breadcrumb mixture neatly over the mussels and slide under a preheated, medium grill, for 2–3 minutes, or until the breadcrumbs are crisp and golden.