1. Preheat oven to 450°.
2. Combine first 5 ingredients and 1/8 teaspoon salt in a small bowl, stirring with a whisk.
3. Place fish, skin side down, on a parchment-lined baking sheet. Rub fish with oil; sprinkle with remaining 1 teaspoon salt and pepper. Bake at 450° for 8 minutes. Remove from oven.
4. Preheat broiler to high.
5. Broil fish 4 minutes or until desired degree of doneness. Sprinkle with chives. Cut fish crosswise into 6 equal portions, top evenly with shallot cream, and serve immediately.