Pat swordfish dry. Season both sides with kosher salt and freshly ground black pepper.

Place flour on a baking sheet and dredge swordfish steaks to coat lightly on both sides, shaking off any excess.

Heat a cast iron skillet over medium-high heat. Add avocado oil and 1 tablespoon butter. When hot and shimmering, place swordfish in the pan and sear until golden brown on each side, about 4 minutes per side. Transfer to a warmed plate and set aside.

Carefully pour off excess butter/oil from the pan. Lower heat to medium, add 1 tablespoon butter, then stir in shallots. Sauté for 30–45 seconds until translucent, adjusting heat to avoid browning.

Deglaze the pan with white wine, scraping up any browned bits. Let reduce by half.

Stir in capers and lemon juice, cooking for 1 minute.

Reduce heat to low and add the remaining 6 tablespoon butter one piece at a time, stirring or swirling to emulsify into a glossy sauce.

Fold in chopped parsley. Taste and season with salt if needed.

Return swordfish to the pan briefly to warm, spooning sauce over top.

Serve immediately, spooning extra sauce over each piece.