Clean mussels. Scrub mussels with a stiff brush under cold running water. Discard any mussels with broken or cracked shells, or any opened mussels that don’t close when you tap their shells. Remove beards which may appear along the hinge side of the shell, using a sharp knife or pulling with your fingers. Set aside in a bowl. One benefit of farmed mussels is that they are generally cleaner than wild caught ones. This is the most time-consuming part of this dish – the rest of it happens quickly.
Heat a large, deep, lidded sautée pan or skillet over medium flame. Add olive oil and one tablespoon of butter and swirl pan to combine. Add shallots and garlic and cook until shallots soften, stirring often to avoid browning, about 3 minutes. Add wine, bay leaf and a generous grind of black pepper and bring to a boil. Do NOT add salt – the mussels will add plenty of briny, salty goodness to the sauce. Taste sauce at the very end to see if you need to add salt. We did not. Add mussels to the pan, crowding them in if necessary, cover and cook undisturbed for 4 to 5 minutes. Check to see if the mussels have opened; if most have not, replace the lid and cook just a minute or two longer.
Transfer mussels to a large bowl with a slotted spoon, discarding any that have not opened, and cover with a towel to keep warm. Increase heat under pan to high and bring sauce to a boil, letting it cook down just slightly, 1 to 2 minutes. Stir in the remaining butter in chunks, swirling pan to melt. Stir in parsley and remove from heat. The sauce will be more like a broth than a thickened sauce, which is exactly what you want. Divide mussels among 4 shallow bowls (pasta bowls are perfect for this), spoon sauce over them. Serve with slices of baguette for sopping up the sauce.