Season fish with salt and pepper. In a large skillet, melt 2 tablespoons butter and heat 1 tablespoon olive oil. Add fish, skin side up. Cook for 3-4 minutes per side (depending on the thickness). Transfer fillets to a plate and cover.
Add in the garlic and sauté for about 20 seconds. Add chicken broth, wine, lemon zest and lemon juice. Allow it to reduce slightly, then add remaining 2 tablespoons butter and whisk until all of the butter is fully incorporated. Sprinkle in the capers, and fresh parsley. Add fish back in the pan and simmer in the sauce for 2 minutes.
Drizzle with remaining 1 tablespoon olive oil and garnish with lemon slices and extra parsley, if desired. Serve immediately. Enjoy!
