Sauce: 

Melt butter in a skillet over medium heat; add onion, white parts of green onion, celery, bell pepper, and garlic. Cook, stirring occasionally, until vegetables are very soft, 12 to 15 minutes (do not brown). Make a well in the center and add tomato paste; cook, stirring tomato paste, until very fragrant, 2 to 3 minutes. Stir the pan through.

Put the cornstarch in a small bowl and add about 1 tablespoon of seafood stock; add remaining stock to pan. Add crawfish tails and fat and bring to a simmer. Season to taste with salt, pepper, and cayenne; cover and cook for 20 minutes. Stir cornstarch to dissolve and add to pan; cook, stirring, until thickened. Remove from heat, cool to room temperature, and refrigerate until needed.

Catfish:

Preheat oven to 400ºF; reheat prepared Evangeline Sauce.

Season fish generously with salt and pepper and place in a rimmed baking pan. Combine butter and lemon juice and pour over fish; transfer to preheated oven and bake until fish flakes easily, 10 to 15 minutes.

Spread rice on a serving platter and top with catfish and drizzle with pan juices. Spoon warmed Evangeline Sauce over the fish and garnish with sliced green onions; serve at once.