Clean the mussels in the sink under running water. Pick up each mussel and check that it's firmly closed.
If you find an open mussel, lightly tap on its shell. If it closes up again, it is still alive but if it doesn't make any move, discard it.
Scrub each mussel clean with a stiff brush to get rid of any debris like barnacles or mud spots and pull off the hairy beard that sticks out from the shell, if it has one. Once they are cleaned, they are ready to cook.
Heat a large pan or a wok on medium heat and add the butter.
Once the butter is melted, add the shallots and garlic, and gently sauté for a few minutes until translucent.
Add the mussels and pour in the wine or brandy. Close a lid and cook them for 2 to 3 minutes or until their shells are all open on high heat. Give the pan a good shake now and then. As the mussels cook, they will release their highly flavored salty water into the pot.
Remove the pan from the heat, remove the mussels on a large bowl using tongs and return the pan to heat. Keep the cooking liquid from the mussels in the pan, do not discard it.
Add the double cream (heavy cream) and freshly ground black pepper to the pan and let it boil for a few minutes, then add the chopped parsley.
Return the mussels to the pan along with the liquid drained from them in the bowl. Avoid adding the grit that settled at the bottom of the bowl.
Close the lid and return the pan to high heat for another minute to finish cooking the mussels. Give the pan a good shake making sure the mussels are all covered with the creamy sauce.
Discard any unopened mussels before serving.