Rinse cod under cold water. Place pieces in large bowl; submerge completely in cold water. Cover bowl with plastic wrap; transfer to refrigerator. Let soak 24-36 hours, changing water every 8 hours. Rinse; using paper towels, pat dry. Cut into four portions; set aside.
Heat oil in medium cazuela (or large, heavy-bottomed skillet) over medium-low heat. Add bacon and onions; cook until onions are very soft and translucent, about 10 minutes. Add pimientos, garlic, paprika; cook until fragrant, about 1 minute more. Transfer pimiento mixture and ½ cup water to bowl of food processor. Puree until mixture is completely smooth, about 2 minutes.
Return sauce to cazuela over medium-high heat. Bring sauce to a boil, reduce heat to medium low and simmer, stirring occasionally, until sauce thickens and begins to caramelize, about 10 minutes.
Add soaked cod to sauce; simmer, covered, until warmed through, flipping once, about 10 minutes. Evenly divide cod and sauce among serving plate. Garnish with parsley, if desired.
Soaking salted cod is a necessary step in ridding the salt used for preservation. After 24 hours of soaking, remove a small flake of flesh, cook on a greased skillet, then taste. The meat should be firm, fresh and flavorful (not salty). If needed, continue to soak the cod in new water. Otherwise, use immediately.