Season swordfish steaks on both sides with 1 tsp Kosher salt and ¼ tsp freshly ground black pepper.
Preheat a large skillet over medium-high heat. Add neutral oil. When the oil shimmers, carefully add the seasoned swordfish steaks then cook, undisturbed. Use tongs or a fish spatula to carefully transfer each swordfish steak to a large serving platter.
Reduce the heat to medium, then add chopped shallot. Season lightly with a pinch of Kosher salt, then cook, stirring occasionally. Increase the heat to medium-high, then add low-sodium chicken broth, then use a spatula to scrape up any browned bits. Allow the sauce to reduce.
Add the juice of lemon and drained capers, then stir well. Remove from the heat, then stir in cold butter. Taste, adjust seasoning with Kosher salt and black pepper as desired, then pour over the swordfish. Garnish with chopped parsley or chives, then serve immediately.