Bring ingredients to room temperature: take the cod out of the fridge 10–15 minutes before cooking. Pat it dry with paper towels. Why: removing surface moisture helps the fish develop a golden brown crust when it hits the pan instead of steaming.

Season the cod generously on both sides with salt and pepper. Zest half a lemon and reserve the zest; then squeeze the lemon half and set the juice aside. Why: seasoning ahead ensures the flesh is flavorful through and through, and zest gives bright aromatics that won’t be lost in the pan sauce.

Heat a 10–12 inch (25–30 cm) skillet (preferably stainless steel or cast-iron) over medium-high heat until it’s hot but not smoking. Add the olive oil and swirl to coat. Why: a properly preheated pan gives the fish an immediate sear and prevents sticking.

Add the cod fillet, presentation side (drier side) down first. Press gently with a spatula for 10 seconds to ensure even contact. Sear without moving for 2½–3 minutes, until the edge closest to the pan turns opaque about 1/3–1/2 of the way up and a golden crust has formed. Why: a short, undisturbed sear promotes Maillard browning which builds flavor and texture.

Flip the cod, reduce heat to medium, and add the butter and capers to the pan. Spoon the melting butter and capers over the fish for 1½–2 minutes until the fish is opaque and flakes easily (target internal temperature ~60–63°C / 140–145°F). Why: finishing with butter adds silkiness; basting distributes heat and infuses the fish with caper-brightness.

Remove the fish to a warm plate and tent loosely with foil to rest while you finish the sides and the sauce. Why: resting lets carryover heat finish the fish gently and keeps it moist.

While the fish cooks, reheat a nonstick or cast-iron pan over medium-high for the potatoes. Add the parboiled, lightly smashed purple potatoes to the dry hot pan with a small drizzle of olive oil or 1/2 tsp butter (you can split the 1 tsp butter between potatoes and sauce). Press them down with the back of a spatula and let them cook undisturbed 3–4 minutes until the exposed flesh is golden and crisp. Flip and crisp the other side 2–3 minutes. Why: parboiled potatoes crisp quickly; pressing creates more surface contact for browning which gives a creamy interior and crunchy exterior.

As the potatoes finish, quickly reheat the blanched broccoli in simmering water or in the microwave (30–40 seconds) or toss briefly in the hot potato pan for 30–45 seconds with a pinch of salt. Why: broccoli is already blanched — you only need to warm it through to retain bright color and a slightly crisp texture.

Make the lemon-caper pan sauce: with the fish removed and the pan still over medium heat, add the reserved lemon juice and scrape any browned bits (fond) from the pan with a wooden spoon. Let the lemon juice simmer 30–45 seconds to deglaze and reduce slightly, then swirl in the remaining butter (or the butter reserved) off heat to emulsify a glossy sauce. Stir in the capers (if you prefer them in the sauce rather than in the basting) and half the chopped parsley. Why: deglazing lifts concentrated flavor from the pan; whisking in cold butter off heat builds a velvety emulsion without breaking.

Plate: spoon a little sauce onto the plate, set the cod on top, spoon more sauce over the cod, scatter crisp smashed purple potatoes to the side, and arrange the blanched broccoli. Finish with lemon zest, the remaining chopped parsley, and an extra grind of black pepper. Why: finishing garnishes add fragrance, visual contrast, and a final burst of citrus that brightens the dish.

Taste and adjust: add a tiny pinch of flaky sea salt to the potatoes and broccoli if needed; capers are salty so check the fish before adding more salt. Serve immediately. Why: balancing salt at the end prevents over-seasoning because capers concentrate saltiness.