In a large pot or deep fryer, heat vegetable oil to 325째F (160째C).
Rinse the potato strips in cold water and pat them dry with paper towels.
Fry the potatoes in batches for about 4-5 minutes until they are soft but not browned. Remove and drain on paper towels.
Increase the oil temperature to 375째F (190째C). Fry the potatoes again in batches until they are golden brown and crispy, about 2-3 minutes. Remove and drain on paper towels, then season with salt.
In a large pot, melt the butter over medium heat. Add the finely chopped onion, minced garlic, sliced leek, and celery. Cook until the vegetables are soft and translucent.
Add the cleaned mussels to the pot, followed by the dry white wine, fish or vegetable broth, chopped parsley, ground black pepper, and bay leaf.
Increase the heat to high, cover the pot, and cook for about 5-7 minutes, or until the mussels have opened. Discard any mussels that do not open.
If desired, stir in the heavy cream for a richer sauce.
Enjoy your meal!