Clean the mussels by thoroughly scrubbing them under plenty of running water, pulling away and discarding the 'beards', the seaweed-like stringy threads. Discard any broken mussels, and any mussels that don't close tightly when you tap them.
Heat the olive oil in a heavy pan with a tight-fitting lid. Add the shallot and garlic and cook over a medium heat until softened, but not coloured.
Add the wine and turn up to a high heat. As the wine starts to boil, add the cleaned mussels and thyme to the pan. Turn the heat down to low.
Put the lid on the pan and allow the mussels to steam. Cook for about 4-5 minutes, lifting the lid from time to time to check - you will know they are cooked when the shells have opened. Discard any mussels that remain closed.
Add the double cream and cook for a further minute.
Scatter with the chopped parsley and serve in deep bowls.