Gently simmering mild fish in a simple, fragrant broth--known in French cooking as a court-bouillon--is a wonderful way to impart flavor. Be careful not to overcrowd or overcook the fish, as either will cause it to fall apart.
To prepare broth: Combine all broth ingredients in a large pot. Bring to a boil, reduce heat to low and simmer, uncovered, for 30 minutes. Strain into a large deep skillet, discarding solids.
To poach halibut & make vinaigrette: Bring broth just to a simmer. Season halibut with salt and pepper on both sides. Add halibut to broth and poach, uncovered, until opaque in the center, 5 to 10 minutes.
Meanwhile, spoon 2 tablespoons of the simmering broth into a small bowl. Add lemon juice, mustard and sour cream. Gradually whisk in oil. Add shallot and season with salt and pepper.
Remove halibut from poaching liquid and divide among 4 warmed plates. Stir parsley, tarragon, chives and chopped dill into the vinaigrette and spoon over the fish. Garnish with dill sprigs. Serve immediately.
Make Ahead Tip: Cover and refrigerate the broth (Step 1) for up to 2 days or freeze for up to 4 months.
5 lean meat, 1 fat