Season the fish.
Pat the tilapia fillets dry and season both sides with kosher salt and freshly ground black pepper.
Heat the pan.
Preheat a large non-stick skillet over medium heat. Add butter and olive oil until melted and hot.
Cook the tilapia.
Place two fillets into the skillet and cook for about 4 minutes.
Flip and finish cooking.
Turn the fillets carefully and cook another 2–3 minutes until the fish flakes easily with a fork.
Remove the fish and repeat with the remaining fillets. Cover loosely with foil to keep warm.
Prepare the sauce.
In the same skillet, add minced shallots and garlic. Cook for 2–3 minutes until soft and fragrant.
Add the liquid.
Pour in the broth and lemon juice. Bring to a gentle boil and cook for 3–4 minutes until slightly reduced.
Stir in capers, lemon zest, and parsley.
Taste the sauce and adjust seasoning with salt and pepper if needed.
Finish the dish.
Return the fish to the skillet and spoon the sauce over the fillets.
Serve the Tilapia with Lemon Caper Sauce with fresh lemon slices and a light drizzle of olive oil.