Pat the halibut fillets dry, season with 1 tsp kosher salt and ½ tsp black pepper, heat 2 tbsp neutral oil in a large skillet over medium-high, and sear the fish for 4 to 5 minutes per side until it reaches 130°F (54°C) internally. Transfer to a plate.

Reduce heat to medium, add 3 tbsp unsalted butter, and swirl until the butter foams and turns amber-brown with a nutty smell, about 2 minutes.

Add 2 cloves minced garlic to the pan and stir for 30 seconds, then add 3 tbsp capers and 3 tbsp lemon juice, scrape up the browned bits, and stir in the remaining 1 tbsp butter until the sauce is glossy, about 1 minute.

Return the fillets to the pan for 30 seconds to warm through, transfer to plates, spoon the caper-butter sauce over each fillet, scatter 2 tbsp chopped parsley on top, and serve with fresh lemon rounds.