For the salmon with arugula and potato puree, first prepare the puree: Peel the potatoes, cut them into pieces and boil them in salted water until soft. Press through the potato press or mash.
Rinse arugula with cold water and shake dry. Chop coarsely and puree with plucked basil leaves and some olive oil in a hand blender.
Heat the milk in a pot and melt the butter in it. Season with salt, pepper and nutmeg. Add potatoes and arugula and stir to a smooth puree.
Rinse the salmon fillets with cold water and pat dry. Acidify with lemon juice and add salt. Heat a mixture of oil and butter in a pan and put the salmon fillets in, flesh side first. Fry for about 4 minutes (depending on the thickness of the fillets), turn and fry on the skin side.
Arrange the salmon fillets on warmed plates and dress with the arugula-pea purée.