Pound steak to 1/2-inch thickness. Slice diagonally across the grain into 1/2-inch-thick slices. Dredge pieces in 1/4 cup flour, and set aside.
Sauté onion in butter in a heavy skillet until tender. Add dredged steak pieces to sautéed onion mixture in skillet; brown steak on all sides. Remove steak from pan, reserving sautéed onion and pan drippings.
Add remaining 1 tablespoon flour to reserved pan drippings mixture; cook 1 minute over low heat, stirring constantly. Gradually add vinegar and water; cook over medium heat 1 minute, stirring constantly. Combine mustard, thyme, paprika, salt, and pepper; mix well. Add spices to pan liquid; bring mixture to a boil, stirring until well blended.
Add steak to gravy; cover and simmer 1 hour and 20 minutes or until meat is tender. Transfer to a serving platter. Garnish with parsley, if desired.