Preheat the oven to 450 degrees F. Place the vermouth, garlic and tarragon in a small pot and simmer until reduced to about 1 Tbsp. Add the cream and simmer until it slightly thickens. Season with salt and pepper, and then remove from the heat. Place the oysters in a baking dish or roasting pan. (If desired, to help the oysters sit level, you could nestle them in a bed of coarse salt.) Top each oyster with a spoonful of the tarragon vermouth cream, and then sprinkle with Parmesan cheese.
Bake for 10 to 12 minutes, until hot and lightly browned. Sprinkle with parsley and serve.