Preheat the oven to 220 degrees. Cut the unpeeled sweet potato into one-centimeter-thick fries, toss them with two tablespoons of olive oil, the paprika, and some salt, and spread them out well on a baking sheet. If they are piled up, they will steam and become soggy. Bake for twenty-five minutes, turning them halfway through.
Meanwhile, rinse the mussels under cold running water and discard any that are open and do not close when tapped. Pull off any remaining beards.
Finely chop the onion, fennel, and celery, and slice the garlic. Heat the butter with the remaining olive oil in a large pot with a lid and sauté the vegetables over medium heat for eight minutes until soft but not browned. Add the garlic and cook for another half a minute.
Pour in the white wine, turn the heat to high, and let it boil for a minute to evaporate the alcohol. Add the mussels, cover with the lid, and shake the pot a few times. They are ready in four to five minutes, as soon as they have all opened. Cooking them longer will make them rubbery, so remove the pot from the heat immediately and discard any mussels that remained closed.
Scatter plenty of coarsely chopped parsley over the mussels and grind some black pepper on top. Serve with the fries and a lemon wedge.