Mix water and mushrooms in large bowl. Let stand 30 minutes. Drain, reserving 1 cup liquid. Finely chop half of mushrooms. Slice remaining mushrooms.
Heat 4 teaspoons oil in medium skillet over medium heat. Add 2 tablespoons shallots and sauté 1 minute. Add chopped mushrooms; sauté 5 minutes. Season stuffing with salt and pepper.
Heat 1 tablespoon oil in large skillet over medium-high heat. Add 4 tablespoons shallots; sauté 3 minutes. Add sliced mushrooms; sauté 4 minutes. Mix in brandy and boil until almost no liquid remains, about 2 minutes. Add wine; boil 3 minutes. Add broth and reserved mushroom liquid, leaving any sediment behind; boil 5 minutes. Add cream; boil until thickened, about 8 minutes.
Cut 2 1/2-inch-wide by 1 1/2-inch-deep pocket in side of each steak. Press 1/4 of stuffing into each pocket. Secure with toothpicks. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add steaks; cook to desired doneness, about 4 minutes per side for medium-rare. Transfer to plates. Add sauce to skillet; bring to simmer, scraping up any browned bits. Spoon sauce over steaks.
