Heat 3 tablespoons of olive oil in a medium saucepan over medium heat. Add the diced shallots and cook for 3-4 minutes, stirring occasionally, until they become translucent and fragrant. Add the minced garlic and cook for 1 minute more, being careful not to burn it. Pour in the dry white wine and let it simmer for 2-3 minutes, allowing the alcohol to evaporate and the flavors to concentrate. This aromatic base will form the foundation of your sauce.
Add the chicken broth to the pan from Step 1 and bring to a gentle simmer. Stir in the chopped tomatoes, black olives, roasted red peppers, and capers. Reduce heat to low, cover the pan, and let the mixture simmer for 10-15 minutes to allow the flavors to meld together beautifully. I like to taste the sauce halfway through simmering and adjust the seasoning—this quiet simmering time is key to developing depth in the sauce while your fish cooks.
While the sauce simmers, season both sea bass fillets generously with salt and pepper on both sides. Heat 2 tablespoons of olive oil in a separate large skillet over medium-high heat until it shimmers. Carefully place the sea bass fillets skin-side up in the hot pan and sear for 4-5 minutes until the bottom is golden and crispy. Gently flip the fillets and cook for another 3-4 minutes until the fish reaches an internal temperature of 135-145°F (I use an instant-read thermometer to check the thickest part). The fish should be opaque and flake easily—don't overcook it or it will dry out.
Transfer the cooked sea bass fillets to a serving plate or individual plates. Remove the Mediterranean sauce from heat and stir in the lemon juice. Taste and adjust the seasoning with salt and pepper as needed—the acidity from the lemon should brighten all the flavors. Pour the warm sauce generously over the sea bass fillets and garnish with the fresh chopped parsley. Serve immediately while the fish is still warm and the sauce is at its best.