Preheat oven to 425F degrees.
In a rimmed baking sheet, coat fish with 2 tablespoons oil. Bake skin side down until flaky, about 10 minutes.
Meanwhile, put remaining oil in a sauté pan over medium-high heat and add peppers, mushrooms, and onion. Cook, stirring frequently, until mostly softened, about 4 minutes.
Add lemon juice and 1/2 teaspoon salt. Cook, stirring frequently, until mixture is thickened and creamy, about 4 minutes. Remove from heat.
Spoon pepper mixture onto plates and top with fish.
Serving Suggestions: Garnish with remaining chives, remaining 1/2 teaspoon salt, and pine nuts, if using.