Preheat the Oven: Preheat oven to 400°F with rack on middle position. In a small pan, combine all Lemon Garlic Mixture ingredients and stir to fully combine. Set aside. This mixture will create a flavorful sauce that will elevate the natural flavors of the swordfish.
Prepare the Fish: Use paper towels to pat-dry all excess moisture from the swordfish fillets. Evenly sprinkle both sides of fillets with pinches of kosher salt and freshly ground black pepper. Set aside. Proper drying ensures a better sear on the fish, while the seasoning will enhance the flavor of the swordfish.
Sear the Swordfish: In a large, oven-proof pan, heat the olive oil over medium-high heat. Once oil is hot, add the swordfish fillets to pan and let cook until browned on one side, about 3 minutes (do not move fish around much). The searing process creates a delicious crust on the exterior while locking in moisture.
Finish in Oven: Carefully flip fish fillets over to the other side, turn stove off, and immediately transfer pan into hot oven. Let fish roast about 5-6 minutes or just until the top is golden and center is just cooked through. Take care not to overcook. This gentle finishing method ensures the fish cooks evenly while remaining moist and tender.
Prepare Sauce and Serve: A minute before fish is done cooking in oven, cook small pan of prepared lemon-garlic mixture over medium-high heat, constantly stirring, just until melted and bubbly. Immediately turn heat off and pour mixture over the cooked fish. Be sure to pour on any juices from the swordfish pan as well. The warm lemon-garlic sauce will coat the fish with rich flavor and a beautiful finish.