1. Soak, clean, and debeard the mussels (see Notes).
2. Place the mussels in a medium-size, nonreactive saucepan or stockpot. Add the wine, shallots, and garlic. Cover the pan and place it over high heat. Steam the mussels until they open, about 5 to 8 minutes, shaking the pot occasionally to redistribute the mussels as they steam.
3. Using a slotted spoon, remove the mussels to a bowl and set them aside, discarding any that haven’t opened. Pour the cooking liquid through a strainer lined with cheesecloth into a heatproof bowl and set aside. When the mussels are cool enough to handle, remove the meat from the shells, discarding the shells. Cover the mussels to keep them warm while you prepare the soup.
4. Rinse out the saucepan and wipe it dry. Add the butter and melt over medium-low heat. Add the onion and carrot and cook gently, stirring occasionally, until softened, about 5 minutes. Reduce the heat to low, stir in the flour, and continue cooking, stirring constantly, until the mixture develops a nutty aroma, about 5 minutes. Be careful not to let the flour brown.
5. Add the mussel cooking liquid, saffron, and chicken stock and whisk well. Bring to a boil over high heat and cook, uncovered, for 15 minutes, to reduce the liquid somewhat and blend the flavors. Reduce the heat so the liquid simmers briskly and whisk in the cream. Cook until slightly thickened, about 10 to 15 minutes, whisking occasionally. Taste the soup. If it’s not the desired strength, continue simmering to reduce it and further concentrate the flavors. Taste again and season with salt (if necessary), cayenne, and lemon juice.
6. To serve, divide the mussels among soup plates and ladle the hot soup over them. Garnish with snipped chives.