Start sauce by heating Baklouti and Smoked Olive Oils in large pot over medium-high heat. Add onion and cook, stirring regularly until onions start to brown, about 5 minutes. Add garlic and stir a bit longer.
Add diced tomatoes, bay leaf, oregano, parsley, half the olives, and half the capers. Simmer briskly, stirring frequently, about 5 minutes to evaporate some liquid. Reduce heat to medium-low, stir in 1/2 cup water and simmer 15 minutes. Taste and season with additional salt and pepper, if desired.
While sauce is simmering, dredge fish fillets first in flour, then in egg, then back in flour. Heat 1/3 cup Extra Virgin Olive Oil in very large (12") non-stick skillet over medium-high heat. Once skillet is hot, pan fry fish approximately 3-4 minutes per side, or until nicely golden brown and a bit crisp on exterior.
To finish, ladle sauce onto individual dinner plates. Place fish in center, garnish with remaining olives, capers, parsley, and green onions. Serve immediately.