For the sauce: In a heavy-bottomed skillet over medium heat, melt the butter and saute the onions, peppers and garlic until wilted. Add the flour and stir until a blond roux is achieved, about 2 minutes. Stir in the sugar, chicken base, crab base, granulated garlic, basil, black pepper, cayenne pepper and thyme. Add the milk and wine and cook over medium heat until the milk thickens, stirring constantly, about 6 minutes. Add the cheese and stir until the cheese melts and fully incorporates into the sauce. Add the crawfish tails and cook until heated through, about 4 minutes. Add the green onions just before serving.
For the catfish: Sprinkle the catfish with Creole seasoning. In a small bowl, beat the eggs and add the milk. Coat the catfish in flour and dip in the milk/egg mixture, then coat with cornmeal. Heat the oil to 350 degrees F in a large skillet. Fry the catfish until golden brown, 7 to 8 minutes.
Serve the catfish with the crawfish au gratin sauce.