Mix the cornmeal and flour in a shallow dish. Season the filets with salt and pepper, dip in the milk and coat with the cornmeal mixture. Melt ½ cup butter in a skillet large enough to hold 4 filets and add the filets.
Cook over medium heat until the filets are light brown on the bottom, shaking the skillet occasionally to keep the filets from sticking. Carefully lift the filets with a large spatula and turn. Cook until brown on the remaining side. Remove the filets to a heated serving platter, reserving the pan drippings.
Increase the heat to medium-high and add the desired amount of additional butter to the reserved pan drippings. Cook just until the butter begins to brown, stirring constantly with a wooden spoon to release any browned bits from the bottom of the skillet. Stir in the wine, lemon juice and green onions and cook until slightly thickened, stirring frequently. Drizzle over the filets and serve immediately.
From Table of Content, reprinted with permission from Junior League of Birmingham, Inc. Table of Contents can be purchased here.