Step 1

Melt 1 tablespoon butter in a large saucepan over medium-low heat. Add leeks, shallot, garlic, and bay leave. Season lightly with salt and heavily with black pepper and cook, stirring, until vegetables are very soft but not browned, about 10 minutes.

Step 2

Increase heat to high and add cider or wine. Bring to a boil and let reduce by half, about 2 minutes. Add mussels, stir, cover, and cook, shaking pan constantly and peeking every 30 seconds to stir. As soon as all the mussels are open, transfer mussels to a bowl using tongs. Place pan lid over bowl to keep mussels warm.

Step 3

Remove from heat and whisk in remaining butter along with mayonnaise or crème fraîche (if using). Return mussels to pot, add parsley, lemon juice, and lemon zest, stir to combine, then transfer to a warm serving bowl. Serve immediately with additional mayonnaise (if using) and broiled bread.