In some places they call the dish Steak Benedict.

EGGS BENEDICT AND STEAK

4 tbsp. butter
1 green onion, chopped
1/2 tsp. salt
1/4 tsp. freshly ground black pepper
4 slices bread, toasted
2 lg. tomatoes, thickly sliced
4 poached eggs (recipe follows)
Tarragon Hollandaise (recipe follows)

Poached Eggs: Heat wide skillet full of water to boiling. Crack eggs, without crowding, into simmering water and cook about 1 1/2 minutes or until done to your liking. Remove with slotted spatula.

Tarragon Hollandaise: Simmer 2 chopped green onions, including tops, in 3 tablespoons tarragon vinegar until vinegar evaporates. Transfer to blender or food processor container. Add 1/2 teaspoon dried tarragon leaves and 3 egg yolks. Turn motor on and slowly drizzle in 3/4 cup hot melted butter. Process until sauce is smooth. Sauce will be fairly thin, but will thicken as it cools. May be used at room temperature. Makes about 1 cup.

Place steaks between sheets of waxed paper or plastic wrap and pound with flat side of mallet until about double in size. Heat 2 tablespoons of the butter in frying pan and add chopped green onion and steaks. Brown over high heat until cooked through. Sprinkle with salt and pepper. Place toast on heated platters. Top with steaks. Keep warm. Add tomatoes to skillet along with remaining 2 tablespoons butter and cook quickly until heated through. Place tomatoes on steaks. Top each with a poached egg. Drizzle with Tarragon Hollandaise. Serve immediately.

Steak-n-Eggs Benedict
A delicious variation on a brunch tradition.
Servings: Serves 4

4 tenderloin steaks, 1/2-inch thick
4 English muffins, toasted and buttered
4 eggs
1 Tbsp. vinegar

Hollandaise Sauce*:
3 large egg yolks
1-1/2 Tbsp. cold water
1/2 cup butter, melted
2-3 tsp. lemon juice
-- salt and pepper, to taste
-- Tabasco, to taste

In nonstick skillet, over medium-high heat, pan-fry steaks until internal temperature reads 140°F for medium-rare, or to desired doneness. Remove from heat, keep warm. To make sauce: Whisk eggs yolks until light and frothy. Pour into top of double boiler over gently simmering water and continue to whisk until eggs are thickened, 2 to 4 minutes. Do not let eggs get too hot. Once thickened, remove from heat. Continue to whisk and slowly add melted butter, lemon juice, Tabasco, salt and pepper. Meanwhile in large saucepan, heat 2 to 3 inches of water until almost boiling. Add vinegar.
Gently crack eggs into four small cups and slide into simmering water. Adjust heat to keep water just below a simmer. Cook until the whites of the eggs are set, but centers are still soft. Remove eggs with slotted spoon.

To assemble: Top each muffin with tenderloin and a poached egg. Pour warm sauce over top. Serve immediately.