In a large mixing bowl, crack an egg and beat it lightly. Add sliced green onions, seasoned bread crumbs, and prepared mustard. Then, gently incorporate ground beef, mixing until just combined. Shape into four patties, approximately 1/2-inch thick.

Preheat an ungreased skillet over medium-high heat. Carefully place the shaped patties in the skillet. Cook for 4-5 minutes per side, flipping when golden-brown and no longer pink in the center. Drain excess fat after cooking.

In a small bowl, combine beef gravy with water and optional prepared horseradish; stir until well-blended. Add fresh mushrooms into the gravy mixture. Pour this rich gravy over the cooked patties in the skillet and simmer uncovered for about 5 minutes, or until mushrooms soften.

Remove beef patties from heat. If desired, sprinkle freshly chopped parsley on top. Serve hot, alongside mashed potatoes, rice, or egg noodles.