Rinse the mussels 2-3 times under cold water, removing any dirt and sand.
Peel the onions and cut each into 8 pieces. Clean the celery and cut the stalks into 2-4 cm pieces.
Heat butter or oil in a large pot over medium heat. Add the onions and celery, and cook for 5 minutes until tender but still firm. Add a splash of white wine or broth if desired.
Increase the heat to medium-high. Add the drained mussels, season generously with salt and pepper, cover with a lid, and cook for 5-10 minutes until all mussels have opened.