Pat the cod fillets dry with paper towels, then season generously with salt and pepper on both sides.
Heat the olive oil in a non-stick skillet over medium heat until shimmering, then gently place the fillets skin-side down if skin-on.
Cook the fish for about 3-4 minutes, until the edges turn golden and the fish releases easily from the pan, then carefully flip using a fish spatula.
Cook for another 2-3 minutes until the fish is opaque and flakes easily when tested with a fork, then remove from the pan and set aside.
Add 1 tablespoon of butter to the same skillet, letting it melt and foam over low heat, then stir in the minced garlic and cook for about 30 seconds until fragrant.
Pour in the white wine or broth, scraping up any browned bits from the bottom of the pan, and simmer for 2-3 minutes until slightly reduced and fragrant.
Meanwhile, zest half the lemon directly into the sauce, then squeeze in the juice of the whole lemon, whisking to combine and brighten the sauce.
Add the remaining 2 tablespoons of butter to the sauce, whisking until smooth and glossy, then taste and adjust with more lemon or salt as needed.
Return the fish to the skillet for about 30 seconds to warm through, then transfer to plates, spoon the lemon butter sauce generously over each fillet, and sprinkle with chopped herbs.
Serve immediately, enjoying the tender fish coated in bright, silky lemon butter, with the pan sauce drizzled over for extra flavor.
