Place 2 muffin halves, cut side up, on each of 4 plates. Divide fried oysters among muffin halves. Using a slotted spoon, remove eggs from skillet, and gently place 1 egg on top of oysters on each muffin half. Top each serving with 1 to 2 tablespoons hollandaise. Sprinkle with chopped parsley, and serve immediately.
4 Steps to Foolproof Poached Eggs1. Add water to a large skillet, filling two-thirds full.2. Bring to a boil over high; reduce heat to medium, and simmer. Stir in vinegar.3. Break each egg into a custard cup; gently slip eggs into water in skillet.4. Cook until desired degree of doneness (3 minutes for runny yolks, or 4 to 5 minutes for cooked yolks).
Pour water to a depth of 1 inch into bottom of a double boiler over medium; bring to a boil. Reduce heat, and simmer. Combine egg yolks and cold water in the top portion of double boiler. Cook, whisking constantly, until foamy and slightly thickened, 6 to 7 minutes. Gradually add 3/4 cup of the clarified butter, about 1 tablespoon at a time, whisking until incorporated after each addition and mixture is thickened.
Whisk in lemon juice, salt, and tasso until blended. (Reserve remaining clarified butter for another use.) Keep hollandaise warm.
Prepare the oysters: Stir together cornmeal and Creole seasoning in a shallow dish. Dredge oysters in cornmeal mixture.
Pour oil to a depth of 1 inch in a Dutch oven; heat to 375°F. Fry oysters, in 2 batches, until golden, 1 1/2 to 2 minutes per side. Transfer oysters to paper towels, and drain well.
Prepare the eggs: See "4 Steps to Foolproof Poached Eggs," below.