Season the Swordfish: Pat the swordfish steaks dry with paper towels. Season both sides with kosher salt and freshly ground black pepper.

Sear the Swordfish: Heat a large skillet over medium-high heat. Add the neutral oil. Once the oil shimmers, carefully add the seasoned swordfish steaks. Cook undisturbed for 4–6 minutes per side, depending on thickness, until a golden crust forms and the fish is opaque throughout. Transfer the cooked steaks to a serving platter and tent with foil to keep warm.

Prepare the Pan Sauce: Reduce the heat to medium. In the same skillet, add the finely chopped shallot and a pinch of kosher salt. Sauté for about 1 minute until softened. Increase the heat to medium-high, then add the chicken broth, scraping up any browned bits from the bottom of the pan. Allow the sauce to reduce by half, about 2–3 minutes.

Finish the Sauce: Add the juice of one lemon and the drained capers to the reduced broth. Stir to combine. Remove the skillet from heat and whisk in the cold unsalted butter until the sauce is smooth and emulsified. Taste and adjust seasoning with additional salt and pepper if needed.

Serve: Spoon the lemon caper sauce over the seared swordfish steaks. Garnish with fresh parsley or thinly sliced chives. Serve immediately with lemon wedges on the side.