Step 1

Preheat the broiler; place the rack about 5 inches from the broiling unit.

Step 2

Whisk eggs in a bowl. Add cream, hot sauce, basil, oregano, black pepper, and 1 tablespoon of the grated Parmesan cheese.

Step 3

Heat oil in a skillet over medium-high heat. Melt the butter in the skillet and swirl it around to coat the pan evenly. Place the oysters in the skillet and brown on both sides, about 1 minute on each side. Let the liquid reduce a bit, about 30 seconds longer.

Step 4

Slowly pour the egg mixture over the oysters, keeping the oysters evenly distributed in the pan. After about 30 seconds, shake the pan slightly but do not stir. After about 3 minutes when the bottom and sides of the eggs begin to set, sprinkle the remaining cheese on top and place the pan under the broiler.

Step 5

Broil until the eggs begin to puff around the edges and the top is nicely browned, 5 to 7 minutes. Remove from the oven; sprinkle with chopped parsley. Serve immediately from the skillet in wedge-shaped pieces.