Digital kitchen scale, chef’s knife, measuring cups, measuring spoons, immersion circulator, large pot or other vessel for setting up a water bath, 2-quart saucepan with lid, rubber spatula, small bowl, citrus reamer, small fine-mesh sieve, paper towels, 2 gallon-size vacuum-seal or high-quality freezer zip-top bags, vacuum sealer (optional), scissors, half sheet pan, pastry brush, 10-inch cast-iron skillet, fish spatula, platter
Assemble your immersion circulator, setting the water to 140 degrees F (60 degrees C). If you like a slightly softer, less steak-y texture for your fish, try going with 135 degrees F (57 degrees C).
Melt the butter in a 2-quart saucepan over medium-low heat, 3 to 5 minutes. Continue to cook, stirring frequently with a rubber spatula, until the butter solids turn light brown, about 5 minutes. Remove from the heat. Measure out 2 tablespoons of the browned butter, place in a small bowl, and cool to room temperature. Leave the remaining butter in the saucepan until you’re ready to make the sauce.
Thinly slice one of the lemon halves into 8 slices. Juice three more lemon halves, which should produce 1/4 cup juice. If you’re shy on juice, juice another half. Strain the juice and set aside for the sauce.
Pat the fish dry with paper towels and season with 2 teaspoons of the salt. Divide between two gallon-size vacuum-seal or high-quality freezer zip-top bags. Place 2 lemon slices on the skin side of each fillet and add 1 tablespoon of the browned butter to each bag, being careful to work butter between the fillets to prevent sticking. Seal the bags using a vacuum sealer set to “gentle” or “moist.”
Transfer to the water bath. If using zip-top bags, let the bags sink into the water so that the air will be squeezed out via displacement. When the mouth of the bag is almost at the water line, carefully seal the bags. Cook the halibut in the water bath for 20 minutes. (If one of the bags floats, carefully reopen and try the sink-and-seal method again.)
Return the remaining butter to medium-low heat and add the almonds. Cook until the butter foams and the foam turns brown, 3 to 5 minutes. Remove from the heat and gradually stir in the lemon juice; the butter will bubble dramatically. Stir in the remaining 1/4 teaspoon salt, cover, and set the butter sauce aside for serving.
When the halibut is finished, remove it from the water bath. Cut the bags open with scissors, then very carefully remove the fish to a paper towel-lined sheet pan and pat dry with additional paper towels. (The dryer the better.) Brush the skin side lightly with some of the oil.
Heat a 10-inch cast-iron skillet over high heat for 3 minutes. Add 2 teaspoons of the oil and swirl the pan to coat. When the oil starts to smoke, add two of the halibut fillets, skin-side down, and brush the flesh side lightly with additional oil. Cook until the skin is browned and crisp, about 1 minute. Carefully flip with a narrow metal spatula or “fish turner” and cook on the second side until golden brown, about 30 seconds. Carefully transfer to a serving platter and repeat with the remaining oil and fillets.
Drizzle the almond and butter sauce over the top of the fish. Garnish with the parsley and serve.
To thaw frozen fish, remove the fish from its packaging, wrap each fillet in plastic wrap, and place in a lidded container. Refrigerate overnight and cook the next day. Do not let the thawed fish sit in the refrigerator for more than 24 hours.