Prep the fish. Pat the cod fillets dry on all sides. This helps them brown and keeps them from steaming.
Season both sides with salt and pepper.
Optional light dredge. If you want a delicate crust, dust the fillets with a thin layer of flour, shaking off the excess. This also helps the sauce cling to the fish.
Heat the pan. Set a large skillet over medium to medium-high heat. Add the olive oil and 1 tablespoon of butter.
When the butter melts and foams, the pan is ready.
Cook the cod. Lay the fillets in the pan, presentation side down. Cook without moving for 3–4 minutes, until the edges turn opaque and the bottom is lightly golden.
Flip gently. Use a thin spatula to flip the fillets. Cook another 2–4 minutes, depending on thickness.
The fish is done when it flakes easily and looks opaque throughout.
Transfer and tent. Move the cooked cod to a warm plate and loosely tent with foil. This keeps it hot and moist while you make the sauce.
Build the lemon butter sauce. Lower the heat to medium-low. Add the remaining 4 tablespoons of butter to the skillet.
Stir in the minced garlic and cook for 30–45 seconds until fragrant, not browned.
Add lemon and extras. Stir in the lemon zest and 2–3 tablespoons of fresh lemon juice. If using, add capers and a pinch of red pepper flakes. Swirl the pan to combine.
Taste and adjust salt, pepper, and lemon as needed.
Finish with herbs. Turn off the heat and stir in the chopped parsley. The sauce should be glossy and balanced—bright, buttery, and lightly garlicky.
Serve. Spoon the sauce over the cod. Add lemon wedges on the side for extra zing.
Pair with rice, roasted potatoes, or a simple green salad.