Place dried porcini in large bowl. Pour 2 cups boiling water over. Let stand until soft, stirring occasionally, about 1 hour. Using slotted spoon, transfer porcini to small bowl. Cool porcini, then chop. Pour porcini soaking liquid into medium bowl, leaving sediment behind. Melt butter in large skillet over medium-high heat. Add shallot and garlic. Stir 15 seconds. Add fresh mushrooms, thyme, and sage. Saute until mushrooms are tender, 6 to 7 minutes. Transfer mushrooms to bowl. Add vermouth to skillet; boil 3 minutes, scraping up browned bits. Add 4 cups stock, fresh-mushroom mixture, porcini, and porcini liquid. Boil 10 minutes. Whisk in creme fraiche. Stir 1/4 cup stock and cornstarch in bowl to dissolve; mix into gravy. Cook until gravy coats spoon, about 5 minutes. Season with salt and pepper. DO AHEAD: Can be made 1 day ahead. Cool, cover, and chill. Rewarm before continuing. Whisk tarragon into gravy and serve.