Heat the olive oil in a heavy large skillet over medium-high heat. Add the tasso and cook, stirring constantly, until heated through, about 3 minutes. Mix in the onions and cook until just softened, about 2 minutes. Stir in the garlic and cook until fragrant, about 30 seconds. Add the cream and bring to a boil over high heat. Add the green onions and Essence. Reduce the heat to medium. Cook until the sauce is thick enough to coat the back of a spoon, about 5 minutes.
Add the oysters and cook just until the edges begin to curl, about 1 1/2 minutes. Season to taste with salt and pepper. Serve immediately.
Yield: about 2 cups