Preheat a griddle or large skillet. Brush the muffins with the butter. Place the muffins on the hot griddle and pan-fry for 2 minutes on each side. Remove the muffins from the griddle and set aside. Using a sharp knife, split the fillets in half, horizontally.
Season the fillets with Essence. Heat the olive oil in a large skillet over medium-high heat. Sear the fillets for 2 minutes on each side for medium-rare. Remove the fillets from the pan and set aside.
In a large skillet, combine the water and vinegar. Season the water with salt. Bring the mixture to a boil. Slide 4 of the eggs into the water. When the water returns to a boil, reduce the heat to low and simmer until the eggs are set, 2 to 2 1/2 minutes. Watch carefully and remove the eggs when the yolks are still soft, and drain on a paper-lined plate. Season the eggs with salt and pepper. Return the water to a boil and repeat the process with the remaining eggs.
In a stainless steel bowl set over a pot of simmering water over medium heat, whisk the egg yolks with the lemon juice, water, mustard, and parsley. Season with salt and cayenne. Whisk the mixture until pale yellow and slightly thick. Be careful not to let the bowl touch the water. Remove the bowl from the pot and, while whisking vigorously, gradually add the butter, little by little, until all is incorporated. Season, to taste, with salt and cayenne.
To assemble, place the steaks on the English muffins. Top the steaks with the poached eggs. Spoon the Hollandaise sauce over the eggs. Garnish the eggs with parsley.
Combine all ingredients thoroughly.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch, published by William Morrow, 1993.