Make the relish: Preheat the oven to 350 degrees F. Spread the walnuts on a baking sheet and bake until toasted, 7 to 10 minutes. Let cool, then finely chop and transfer to a bowl. Add the cayenne, lemon juice, honey, roasted red pepper, walnut oil, 1 tablespoon olive oil and 2 tablespoons parsley. Add 1/2 teaspoon salt and black pepper to taste and toss to combine. (The relish can be made up to 1 day ahead; cover and refrigerate.)
Make the salmon: Raise the oven temperature to 425 degrees F. Combine the remaining 1 tablespoon olive oil and 2 tablespoons parsley, the chives, lemon zest, 1/2 teaspoon salt, and black pepper to taste in a bowl. Rub the herb mixture all over the salmon. Lay skin-side down in a baking dish and roast until just cooked through, 12 to 14 minutes. Let rest 5 minutes, then transfer to a platter and top with the walnut-pepper relish.