Submerge the salt cod in a large container of cold water for 24 hours, replacing the water at least four times to effectively desalt the fish.
Drain the cod, remove any remaining skin or bones, and cut into 3-inch uniform portions. Pat thoroughly dry with paper towels.
Using a stand mixer or hand whisk, beat the egg whites until stiff peaks form. Gently fold in the egg yolks and flour until a consistent, airy batter is formed.
Heat one tablespoon of olive oil in a wide non-stick skillet over medium-high heat. Dip each cod portion into the egg batter and sear for 2 minutes per side until golden. Remove and set aside.
In a large heavy-bottomed pot, heat the remaining tablespoon of olive oil. Sauté the diced onions and garlic until the onions are translucent and aromatic.
Incorporate the tomato puree, roasted bell pepper strips, oregano, and bay leaves. Simmer the sauce uncovered for 15 minutes over medium-low heat to reduce and concentrate.
Add the capers, olives, and black pepper to the sauce mixture.
Carefully nestle the battered cod pieces into the sauce. Cover the pot and simmer on low heat for 20 minutes, allowing the cod to cook through and the batter to absorb the sauce flavors.
Discard the bay leaves and garnish with fresh parsley before serving.
Serve immediately, ideally with a side of steamed vegetables or a small portion of white rice.