Pat the conger eel fillets dry with paper towels, season generously with salt and pepper, and set aside.
In a large skillet or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and cook, stirring occasionally, for 8–10 minutes, until soft and translucent.
Add the sliced garlic and cook for 1–2 minutes, stirring, until fragrant but not browned.
If using flour, sprinkle the level tablespoon over the onions and garlic and cook for 1 minute, stirring, to toast the flour.
Pour in the white wine, increase heat to medium-high, and cook for 2–3 minutes, stirring and scraping up any browned bits, until most of the alcohol has evaporated.
Stir in the crushed tomatoes and saffron threads (if using). Reduce heat to medium-low and cook for 5 minutes.
Add the fish stock (or water) and bring to a simmer. Cook gently for 10 minutes, then taste and season with salt and pepper as needed.
Nestle the conger eel fillets into the sauce, spooning sauce over them to cover. Simmer over medium-low heat for 8–12 minutes, or until the fish is opaque and cooked through.
Remove from heat, sprinkle with chopped parsley, and let rest for 2 minutes before serving.