Pat the 4 salted cod fillets dry with paper towels and set them aside.
In a large skillet or shallow pan, heat the extra-virgin olive oil over medium heat. Add the chopped onion, sliced garlic, and diced bell pepper, and cook over medium-low heat, stirring occasionally, until the vegetables are soft and translucent, about 10 to 15 minutes.
If using white wine, add it now, increase the heat to medium-high, and cook until the alcohol evaporates, about 2 minutes. Stir in the crushed tomatoes and sugar, then reduce the heat to medium-low and simmer, uncovered, until the sauce thickens, about 15 to 20 minutes.
Season the cod lightly with salt and freshly ground black pepper (taste the sauce before adding more salt). Nestle the fillets into the sauce, skin-side up. Cover and cook over low heat until the fish flakes easily with a fork, 8 to 10 minutes.
Remove from heat, sprinkle with chopped parsley, and serve with boiled potatoes, white rice, or crusty bread.