1. For the fish: Preheat the oven to 175 degrees F. Put the catfish fillets on a rimmed baking sheet and pat dry. Combine the oregano, paprika, Cajun seasoning, sugar, cayenne, salt and pepper in a small bowl. Completely coat the fillets generously with the spice mixture. Set aside for 10 minutes to allow the rub to penetrate.
2. Heat the vegetable oil in a large cast-iron skillet over high heat until almost smoking. Lay 2 fillets in the skillet and cook until deep golden brown and starting to turn black, 3 to 5 minutes depending on the thickness of the fish. Flip and cook another 3 to 5 minutes. Remove to a clean baking sheet and place in the oven to keep warm. Repeat with the remaining fillets, adding more vegetable oil if necessary.
3. For the sauce: Melt 2 tablespoons of the butter in a large skillet over medium heat. Cut the remaining 4 tablespoons butter into small pieces and refrigerate. Add the Cajun seasoning, red pepper flakes, garlic, celery, onions and bell peppers to the skillet, and cook until the vegetables are soft, about 10 minutes. Add the mushrooms and cook until they have released their juices, 10 minutes. Add the mustard and stir to coat. Pour in the wine and cook until almost completely absorbed, 5 minutes. Sprinkle with flour and cook, stirring, about 1 minute. Whisk in 1 cup of water, and then add the shrimp and crabmeat. Simmer until the shrimp are pink, 5 minutes.
4. Whisk in the cold butter pieces, one piece at a time, whisking until each piece melts before adding another. Stir in half of the chopped parsley and the lemon juice just before serving.
5. Ladle about 1/2 cup of the Pontchartrain sauce into each of 4 shallow bowls, top with a catfish fillet, sprinkle with the remaining parsley and serve with lemon wedges.
NotesCook's Note: Resist the urge to flip the catfish too soon; allow the seasonings to blacken and burn onto the fish. Catfish is meaty, so make sure it is fully cooked through.