Clean the mussels by scrubbing them with a brush under running water. Pull off the beard (the whiskery hairs protruding from the shell) by pulling toward the hinge-end of the shell. Discard any mussels that are broken or don’t close their shells when tapped.

Melt the butter in a large stockpot or Dutch oven with a lid. Add the shallots and garlic and cook for just a minute or two, until fragrant. Add the thyme, bay leaf and white wine and simmer for 2 to 3 minutes to let the flavors blend and the liquid reduce to about half.

Increase the heat to high, add the mussels and cover with the lid. Shake the pan every once in a while, and steam the mussels for 3 to 5 minutes until they open.

Remove the mussels from the pan with a slotted spoon or tongs and place in serving bowls, discarding any mussels whose shells did not open during cooking or that have cracked or broken shells. Remove the bay leaf and thyme sprigs from the steaming liquid and stir in the parsley, black pepper and a squeeze of lemon juice. Remove the pan from the heat and add the heavy cream (if using). Pour this over the mussels and serve immediately with crusty bread or French fries to soak up the tasty liquid.