Trim fat from beef. In a small bowl stir together 2 tablespoons of the Dijon-style mustard and the pepper; rub onto the beef. Place the beef on a rack in a shallow roasting pan. Insert a meat thermometer. Roast beef in a 325 degree F oven until thermometer registers 140 degree F for medium-rare (1-1/2 to 2 hours) or 155 degree F for medium (1-3/4 to 2-1/4 hours). Cover with foil; let stand for 15 minutes before carving. (The temperature of the meat will rise 5° during standing.)
Meanwhile, for sauce, in a medium saucepan combine the mushrooms, beef broth, onion, water, garlic, Worcestershire sauce, and thyme. Bring to boiling; reduce heat. Simmer, covered, about 5 minutes or until vegetables are tender. In a small bowl stir together milk and remaining Dijon-style mustard; gradually stir into flour. Add to mushroom mixture in saucepan. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 1 minute more.
To serve, thinly slice beef across the grain. Arrange on a serving platter. Spoon some of the sauce over beef. Pass remaining sauce. Makes 8 to 10 servings.