Pat cod fillets dry on both sides with paper towels. Season evenly with salt, black pepper, and paprika if using.

Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until the oil shimmers.

Place cod fillets in the pan. Cook without moving for 3 to 4 minutes until the bottom is golden and the fish releases cleanly from the pan.

Flip fillets carefully using a thin spatula. Cook for another 2 to 3 minutes until the flesh is opaque and flakes easily at the thickest point. Transfer to a plate.

Reduce heat to medium-low. Add remaining 2 tablespoons of butter to the same pan. Once melted, add minced garlic and cook for 30 seconds until fragrant, stirring constantly.

Pour in lemon juice and add lemon zest. Stir to combine and let the sauce bubble for 1 minute, scraping up any browned bits from the pan.

Return cod to the pan. Spoon the garlic butter sauce over the fillets for 1 minute until heated through. Remove from heat, scatter parsley on top, and serve immediately.