Zest the lemon. Juice half the lemon, then cut the other half into wedges for serving; set aside.
Set a medium dutch oven or heavy pot over medium heat, and melt 3 tablespoons unsalted butter.
Once melted, add 5 cloves garlic, finely minced, lemon zest, and 2 shallots, finely chopped, and reduce the heat to medium-low.
Saute until garlic and shallots are soft and translucent, about 8 - 10 minutes (you’ll want to avoid getting any color on the garlic and shallots here). Season with a pinch of Salt and black pepper.
Whisk 1 tablespoon all-purpose flour into the pan until no clumps remain, and continue whisking for about 1 - 2 minutes until mixture thickens into a golden paste and there is no raw flour smell.
Add in ½ cup clam juice (or fish stock) and 1 teaspoon dijon mustard, and bring mixture to a boil, whisking frequently to ensure the paste fully melts into the liquid. Scrape up any bits at the bottom.
Reduce heat to a simmer, then stir in 1 cup heavy cream. Season again with salt and pepper.
Add the cleaned 2 pounds mussels and half of the parsley to the pot, stirring to combine. Cover pot with a lid, and let mussels simmer on medium heat. Steam until fully opened, about 5 minutes. Once opened, transfer the mussels to a serving bowl with a slotted spoon. Continue steaming any remaining mussels until opened, about 2 - 3 minutes. If you still have unopened mussels after 10 minutes of steaming, discard them (they're dead).
Taste the broth. It should have subtle lemony aroma, with notes of garlic, and a slightly thickened texture. Season with salt and pepper as needed. If the broth tastes watery, you can simmer it for an additional few minutes to thicken it up.
Remove the pot from the heat, then stir in a bit of the reserved lemon juice, to taste. Add more if desired. Transfer the broth and remaining mussels to the serving bowl. Garnish with the remaining parsley. Serve immediately, with a side of lemon wedges and crusty bread.
Notes
To prevent any mussels from overcooking, I typically check on the mussels after 5 minutes, then transfer any already opened mussels to a serving bowl. I then continue simmering the remaining mussels until opened. Any mussels that don’t open after 10 minutes of steaming should be discarded.Do not substitute heavy cream for a lighter dairy product, as it will curdle. Additionally, make sure to add the lemon juice only after removing the cream sauce from the heat.Storage: Store leftover mussels in cream sauce in an airtight container for 2 to 3 days. Personally, I prefer to eat leftover mussels within a day of cooking.Reheating Instructions: Separate the shells from the meat. Meanwhile, reheat the broth on the stove on a low simmer until hot. Add the meat to the broth, then cover the pot and allow to simmer until warmed through. Note: In reheating the mussels again, they may taste slightly chewier as it can be slightly difficult to prevent them from overcooking.