This is a simple but delicious way to prepare halibut, and our brightly colored and subtly flavored sauce creates a beautiful presentation. Fresh carrot and citrus juices are reduced with ginger and lemongrass to form a concentrated base, then cold butter is whisked into the reduction, one tablespoon at a time, to emulsify and enrich the sauce. Meanwhile, the halibut is finishing in the oven after a quick sear to give it some color. The sauce also partners well with other white fish, such as swordfish, cod, mahi-mahi, or scallops.
Place the carrot juice, orange juice, ginger, and lemongrass in a pan and reduce to 2/3 cup over medium-low heat. Discard the ginger and lemongrass, and set the reduction aside.
Position a rack in the middle of the oven and preheat to 400 degrees F.
Place the flour on a flat plate and season with salt and pepper. Dip one side of each fish fillet in the seasoned flour mixture.
Just before you begin cooking the halibut, reheat the carrot juice reduction over medium heat until hot, but not boiling. Stir in the lime juice, then add one tablespoon of butter and whisk until it’s combined. Reduce the heat to low and whisk in each additional tablespoon of butter, one at a time, to emulsify the sauce. When all the butter has been added, stir in the lime zest and season to taste with salt and pepper. Keep warm but do not allow the sauce to get too hot or it will break (the butter will liquefy).
Place a large ovenproof skillet (preferably cast-iron) over high heat. When the skillet is very hot (just below the smoke point), add the sesame oil. Arrange the fillets, floured side down, in a single layer. Cook until the bottom of the fish is seared and golden, 2 to 3 minutes. Remove the pan from the stove and turn the fillets over with a spatula. Transfer the skillet to the preheated oven and roast until the halibut is cooked, 3 to 6 minutes depending on the thickness of the fillets. The residual heat from the pan will continue to cook the fish, so watch carefully and remove the skillet when the fillets are just opaque.
Divide the halibut among 4 warm plates and top each serving with some of the sauce and a sprinkling of parsley, if you like.