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.