How to Make It
Preheat the oven to 400°. In a large saucepan, cover the potatoes with water and bring to a boil. Cook over moderately high heat until barely tender, about 12 minutes. Drain and cool, then cut the potatoes into 1-inch dice.
Brush a large rimmed baking sheet with olive oil. Overlap the leaves on the baking sheet to form an oval 4 inches larger than the salmon fillet. Season with salt and pepper. Set the salmon on the leaves, brush with olive oil and season with salt and pepper. Fold the leaves over the top of the salmon and cover with more leaves if needed. Brush the leaves with more olive oil and season with salt and pepper. Bake the salmon for about 20 minutes, until the fish is just cooked through and the leaves are crisp.
Meanwhile, in a large skillet, heat the remaining 3 tablespoons of olive oil. Add the potatoes and cook over moderately high heat until browned on the bottom, about 4 minutes. Stir and cook until browned all over, about 6 minutes longer. Season with salt and pepper and toss with the parsley and garlic. Cut the wrapped salmon into 6 portions and serve with the potatoes.