Make the sauce first. Heat one tablespoon of oil in a skillet over medium high heat until it shimmers. Add green onions, mushrooms, garlic, tomatoes, and andouille, and cook for about two minutes.
Add the wine and lemon juice and bring it to a boil. Then add the crawfish. Cook until the liquid is reduced by half.
Lower the heat to almost nothing and add the butter in big chips, a little at a time. Work the butter into the sauce by agitating the pan. Remove from heat and season to taste with Creole seasoning and salt. Remove the pan from the heat and cover.
Stir the salt, pepper, and cayenne into the flour. Dust the catfish fillets very lightly with the seasoned flour.
Mix the cornmeal with the salt, pepper, and cayenne. Beat the eggs and mix with the milk. Dip the catfish fillets into the egg wash, shake off excess, then dredge through the seasoned cornmeal.
Heat the oil in a heavy skillet until it shimmers. Saute the catfish until lightly brown on both sides, turning only once. (About two minutes per side). Drain on paper towels for no more than fifteen seconds.
Place two fillets on each plate, with the sauce between them. Warm the sauce a little if necessary.