1. First check through the mussels, discarding any that are cracked or do not close when tapped sharply. Remove any 'beards' and rinse under cold running water.
2. In a large, deep pan with a lid, melt the butter with the olive oil. Add the shallots, cover and cook gently for 10 minutes, until softened and translucent.
3. Add the garlic and cook for a further 2 minutes. Pour in the white wine, bring to the boil and add the mussels. Cover and cook for 4 minutes.
4. Tip the mussels out into a colander set over a bowl to catch the liquid. Return the liquid to the pan and reduce slightly. Add the double cream, season and boil for 2 minutes.
5. Meanwhile transfer the mussels to a large serving bowl, discarding any that have not opened during the cooking process.
6. Add the parsley and chives to the sauce and pour over the mussels. Serve with plenty of warm, crusty bread.