Wash mussels thoroughly under cold running water. Discard any with broken shells or any that are already open and do not close when tapped lightly.
Trim and peel the shallots, carrots, and leeks, then cut them into fine strips. Finely chop the 3 garlic cloves.
Melt the 100 g butter in a large saucepan over medium heat until foaming. Add the shallots, carrots, and leeks and sauté for 2–3 minutes without letting them brown. Stir in the garlic and cook for 30 seconds. Season with salt and pepper and add the 2 bay leaves. Pour in the 0.5 liter white wine and stir to deglaze. Bring to a boil over medium-high heat, then taste and adjust seasoning.
Add the cleaned mussels to the boiling stock, cover with a lid, and cook for 10 minutes over medium-high heat, gently shaking the pan occasionally. Stir in the 0.25 liter cream and the chopped parsley. Taste and adjust seasoning, adding a splash of vegetable broth if needed for more cooking liquid.
Serve the mussels in deep bowls with the cooking liquid. Accompany with fresh baguette.