Heat the vegetable oil in a heavy pot over medium heat until shimmering, 2–3 minutes, then whisk in the all-purpose flour and cook, stirring constantly, until a medium brown roux forms the color of peanut butter, 8–12 minutes.
Add the onion, celery, and green bell pepper and cook, stirring, until softened and starting to brown at the edges, 8–10 minutes.
Stir in the garlic and cook until fragrant, about 1 minute, then add the tomato paste and cook, stirring, 1–2 minutes to caramelize.
Pour in the canned crushed tomatoes and seafood stock, stirring to combine, and bring to a gentle simmer.
Add the bay leaves, dried thyme, paprika, cayenne pepper, black pepper, kosher salt, and Worcestershire sauce; reduce heat to low and simmer, partially covered, 20–25 minutes until the flavors meld and the sauce thickens slightly.
Add the catfish fillets, cut into 2-inch pieces, submerging them in the sauce; simmer gently without boiling until the fish is opaque and flakes easily, 10–12 minutes.
Turn off the heat and stir in the lemon, green onions, and flat-leaf parsley; let rest 5 minutes.
Spoon the couvillion over cooked white rice. Offer hot sauce for serving.