Peel, wash and cut the potatoes into pieces. Cook in boiling salted water for about 20 minutes. Wash parsley, dab dry and remove leaves. Take the fish fingers out of the package.
Wrap 1 slice of parsley leaf around each fish stick. Roast the pine nuts in a large pan without fat, take them out. Heat the oil in the hot pan. Fry fish fingers on each side for 3-4 minutes.
Heat milk and fat. Drain the potatoes, add the milk mixture and mash into puree with a potato masher. Season to taste with salt and nutmeg. Stir the pesto loosely into the puree. Arrange the fish fingers with the puree.
Sprinkle with pine nuts and garnish with basil.