Preheat the oven to 450 degrees F. Toss the leeks in a roasting pan with 1/3 cup olive oil; season with salt. Roast until slightly golden, about 30 minutes.
Meanwhile, place the salmon in another shallow pan and rub with the remaining 1 tablespoon olive oil. Set aside to come to room temperature.
When the leeks are done, reduce the oven temperature to 275 degrees F. Season the salmon with salt, place over the leeks and brush with the oil in the pan. Roast until firm, 30 to 40 minutes.
Meanwhile, cook the potatoes in a pot of boiling salted water until fork-tender, about 10 minutes; drain.
Pulse the shallot in a food processor until minced. Add the butter, chives, tarragon, parsley, lemon juice, and salt to taste and pulse until combined.
Remove the salmon from the oven and top with half of the herb butter; top the potatoes with the rest. Slice the salmon, season with salt and serve with the leeks and potatoes
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