In a large heavy-based pot, heat the butter and olive oil over medium heat. Sauté the shallots until softened, about 3 minutes.
Add the garlic and thyme stalks and cook for a further minute, stirring so the garlic doesn't colour.
Pour in the white wine and add the cleaned mussels. Put the lid on and steam for about 3 minutes until the shells have opened.
Using a slotted spoon, scoop the mussels and thyme stalks out of the pot and set aside. Discard the thyme and any mussels that have not opened.
Add the cream to the liquid remaining in the pot. Let it bubble gently over low heat, stirring, until the sauce has reduced slightly and thickened a little, about 3 to 4 minutes.
Stir in half the parsley. Add the mussels back in and toss to reheat for 1 to 2 minutes.
Scatter over the remaining parsley and lemon zest. Add the lemon juice if using. Serve immediately in deep bowls with crusty bread and a glass of cold white wine.