In a large saucepan of boiling salted water, cook the potatoes until tender, about 15 minutes.
Meanwhile, combine the cream and 4 tablespoons of the butter in a medium saucepan and simmer over low heat until reduced to 1 cup, about 15 minutes.
Drain the potatoes and return them to the saucepan. Shake the pan over high heat for about 30 seconds to dry out the potatoes. Remove from the heat and mash the potatoes with a potato masher. Add the reduced cream and stir in the onions, scallions, capers and dill. Season with salt and pepper, cover and keep warm.
Preheat the oven to 450°. In a large ovenproof skillet, warm the oil over high heat. Season the salmon with salt and pepper and when the oil is hot, add the fillets, skin side down. Add the remaining 2 teaspoons of butter to the skillet, shaking the pan to incorporate the butter into the oil. Cook the salmon for 4 minutes, then transfer the skillet to the oven without turning the fillets. Roast for about 5 minutes, depending on the thickness of the fish.
Spoon the mashed potatoes onto warmed dinner plates and place the salmon fillets on top, skin side up. Sprinkle with the chives and parsley and serve at once.
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