Prep the fish: Pat the tilapia dry on both sides.
Season generously with salt and black pepper. Zest the lemon, then cut it in half and set aside.
Heat the pan: Set a large skillet over medium-high heat. Add the olive oil and 1 tablespoon of butter.
When the butter foams and smells nutty, the pan is ready.
Cook the tilapia: Add fillets in a single layer without crowding. Cook for 2–3 minutes per side, depending on thickness, until the fish turns opaque and flakes easily. Transfer to a plate and tent loosely with foil.
Make the sauce: Lower heat to medium.
Add the remaining 2 tablespoons butter to the skillet. Stir in the garlic and cook for 20–30 seconds until fragrant, not browned.
Add lemon and extras: Stir in lemon zest and squeeze in the lemon juice. Add capers and red pepper flakes if using.
Swirl the pan to emulsify the sauce. Taste and adjust with salt or more lemon if needed.
Finish: Return the fish to the pan for 30 seconds, spooning sauce over the fillets. Sprinkle with fresh parsley.
Serve: Plate the tilapia and pour the sauce over the top.
Add lemon wedges on the side. Serve immediately with your favorite sides.