Preheat the oven to 400 degrees F. Butter a 13 by 9-inch rectangular baking dish.
Heat the olive oil in a saute pan over medium-high heat. Add the onions and celery and saute for 2 minutes. Add the eggplant and peppers and saute for 3 to 5 minutes, or until the vegetables are soft. Season with salt and cayenne. Add the garlic and green onions and saute for 2 minutes. Stir in the chopped oysters and saute for 1 minute. Remove from the heat.
In a large mixing bowl, whisk the oyster liqueur, eggs, and cream together. Add the oyster mixture, bread cubes and cheese and mix well. Reseason with salt and cayenne. Pour the dressing into the prepared pan and cover. Bake for 30 minutes. Remove the cover and bake for an additional 15 minutes, or until the dressing is set in the center. Remove from the oven and cool slightly before serving.