1. Preheat the oven to 450°. In a large enameled cast-iron or stainless steel baking dish, toss the mushroom caps with the wine and 2 tablespoons of the olive oil. Season with salt and pepper. Turn the caps stemmed side down and roast for 10 minutes, or until they release their liquid. Pour the liquid into a glass measuring cup. Turn the mushrooms and roast for 10 minutes longer, or until well browned on the bottom.
2. Transfer the mushrooms to a large plate. Set the baking dish over moderately high heat and when it starts to smoke, add the water. Bring to a boil, scraping up the browned bits on the bottom, and simmer until the water reduces by half, about 3 minutes. Pour the liquid into the measuring cup.
3. Return the mushroom caps to the baking dish, stemmed side up. In a bowl, combine the Roquefort with the cream, anchovies, garlic and mustard. Stir in the bread crumbs and season with salt and pepper. Stuff each mushroom cap with a heaping teaspoon of filling.
4. Season the sirloin roast with salt and pepper. Set a large ovenproof skillet over moderately high heat for a few minutes. Add the remaining 1 tablespoon of olive oil and when it starts to smoke, add the roast, fat side down. Cook until the fat is deeply browned, about 5 minutes, then quickly sear the roast for 1 minute on each side. Turn the roast fat side up and cook for 1 minute.
5. Roast the sirloin in the oven for about 20 minutes, or until an instant-read thermometer inserted in the thickest part registers 120° for rare. Transfer the meat to a carving board and let rest for at least 10 minutes before carving.
6. Meanwhile, preheat the broiler. Set the skillet over moderately high heat. Add the balsamic vinegar and bring to a simmer, scraping up the browned bits from the bottom of the skillet. Add the soy sauce and the reserved mushroom liquid and boil for 3 minutes.
7. Remove the skillet from the heat and swirl in the butter. Season the sauce with salt and plenty of pepper and pour it into a warmed gravy boat. Broil the mushrooms for 3 minutes, or until browned. Rotate the baking dish as necessary. Carve the roast into 4 thick slices and serve with the stuffed mushrooms. Pass the sauce at the table.