Clarify the butter: Preheat oven to 350 F. In a 4-quart, oven-safe saucepan, melt butter over medium heat and bring to a simmer, 5-7 minutes. Once white foam (milk solids) begins to form on the top, skim it off with a small ladle or spoon. Reduce heat to medium-low and continue skimming the milk solids until the butter is clear. Pour the clarified butter through a cheesecloth-lined strainer to catch the smaller milk solids. Set aside to cool to 155 F.
Poach the fish: Season the fish on all sides with salt, about ¼ teaspoon per fillet. Gently lower the halibut into the clarified butter so all four fillets are submerged. Place the fish in the oven and bake, uncovered, 8 minutes.
Assemble the dish: Fish is done when it’s firm but not hard to the touch. Use a slotted spoon to remove the fish, drain off the butter, and plate. Serve with lemon wedges, crunchy salt, and dill.
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