Rinse mussels in cold water, cover with hot water adding onion and parsley root in advance.
Cook and take meat out of mussels.
For the sauce: pound butter with flour, stir in filtered mussels broth and cook thoroughly for 10 minutes.
Season the sauce with lemon juice to taste, salt, sugar and pepper.
Mix the sauce with cooked mussels.
Fill mussel shells with the mixture, drizzle with oil and bake in the oven.
Garnish with lemon and greens.