Rinse mussels under cold running water. Discard any with cracked shells or that remain open when tapped. Remove beards by pulling toward the hinge. Set cleaned mussels in a colander to drain.

Prepare aromatics

Peel and finely mince the shallots and garlic. Zest the lemon and then juice it. Chop parsley and slice chives; keep herbs separate so they can be added at different stages.

Liquid & Seasoning

Sweat aromatics

In a large wide pot or deep skillet with a tight-fitting lid, heat the olive oil and 1 tablespoon butter over medium heat until shimmering. Add shallots and a pinch of salt; cook 3–4 minutes until softened and translucent but not browned. Add the minced garlic and red pepper flakes; cook 30–45 seconds until aromatic.

Deglaze & build broth

Pour in the white wine to deglaze the pan, scraping up any bits from the bottom. Bring to a simmer and reduce for 2 minutes to concentrate flavor. Add fish or shellfish stock (if using) and bring back to a gentle simmer. Taste and season with about 1 teaspoon coarse sea salt and 1/2 teaspoon freshly ground black pepper, adjusting to preference.

Add mussels & steam

Increase heat to medium-high. Add the drained mussels to the pot and give them a quick toss to submerge in the liquid. Cover with the lid and steam for 4–6 minutes, shaking the pot once or twice, until mussels have opened. Discard any mussels that remain closed after 6 minutes.

Finish broth

Remove lid and reduce heat to low. Stir in the remaining 2 tablespoons butter and the heavy cream (if using) to enrich the sauce. Add lemon zest and lemon juice, then fold in most of the chopped parsley and all of the chives, reserving a little parsley for garnish. Taste and adjust seasoning with more salt, pepper, or a squeeze of lemon as needed.

To Serve

Transfer mussels and broth to warmed shallow bowls or leave in the pot for family-style service. Sprinkle remaining parsley over the top. Serve immediately with crusty bread for soaking the broth and melted butter for the bread if desired.

Estimated leftovers/storage: Cool any leftover mussels quickly, store mussels and broth together in a sealed container in the refrigerator for up to 24 hours. Reheat gently on the stovetop; do not overcook to avoid rubbery mussels.