Rinse and clean the mussels in cold water, tugging off any beards and discarding any with badly broken shells. (Don’t worry about open or closed ones at this point.)
Put in a large pan with the garlic, parsley stalks (they’re easier to pick out if you leave them in one piece) and wine, cover and cook over a medium-low heat, shaking the pan occasionally to move the mussels around, until the shells open.
Drain the mussels through a fine sieve set over a heatproof bowl to catch the cooking liquor. If you’d like to serve the mussels on the half shell, or shelled full stop, do this now, working quickly so they stay warm. Discard any shells that have remained tightly closed.
Melt the butter in a medium pan and fry the shallots until soft. Stir in the curry powder, cook for a minute or so, then add the mussel cooking liquid and bring to a simmer. Bubble until reduced by about half. Meanwhile, finely chop the parsley leaves.
Take the pan off the heat and stir in the cream.
Season to taste, then divide the mussels between bowls and pour over the sauce (or stir the shelled mussels into the sauce before serving). Scatter with chopped parsley and eat immediately.