Wash and clean the mussels thoroughly. Discard opened mussels. Boil up wine and 100 ml water in a large pot. Season with salt and pepper. Add the mussels and simmer at medium heat for about 8 minutes until the mussels open
Place the mussels and cooking liquid in a sieve. Collect the stock. Discard unopened mussels. Remove the mussels from their shells. Reduce brew in a pot to approx. 4 tbsp.
In the meantime, prepare the pasta in boiling salted water according to the instructions on the packet. Peel garlic and chop coarsely. Wash basil, shake dry. Puree nuts, oil, garlic, basil, except for a few leaves for garnishing, and reduced cooking liquid with a hand blender
Mix pesto and mussels in a pot for 1-2 minutes at medium heat. Drain the pasta and arrange on plates with the mussel and hazelnut pesto. Garnish with basil leaves