Reduce white wine with shallots, garlic, and thyme. Season with salt and pepper to taste. Add the Tabasco and bring to boil. Whisk ⅓ of the butter at a time, whisking until completely combined. Finish with parsley.
Cool the sauce down in ice bath promptly. Stir it once in a while as it cools. Sauce can be made up to 3 days in advance.
Heat a broiler to high. Place 1 tablespoon of the sauce on top of each of the freshly shucked oysters and sprinkle with freshly grated Parmesan. Place under the broiler until golden. Serve hot.