1. Process bread slices in a food processor 10 seconds or until finely chopped. Place breadcrumbs in a mixing bowl; add ground round and next 4 ingredients. Gently combine until blended, using your hands. Shape into 4 (4-inch) patties.
2. Whisk together brown gravy mix and 1 1/2 cups water.
3. Cook patties in hot oil in a large skillet over medium-high heat 2 minutes on each side or just until browned. Remove patties from skillet. Add mushrooms and onion to skillet, and sauté 6 minutes or until tender. Stir in prepared gravy, and bring to a light boil. Return patties to skillet, and spoon gravy over each patty. Cover, reduce heat to low, and simmer 8 to 10 minutes.
Note: To make ahead, proceed with Step 1 as directed. Wrap each patty individually in plastic wrap, and place in a large zip-top plastic freezer bag. Freeze up to 3 months. Thaw frozen patties in refrigerator 8 hours; proceed with Steps 2 and 3.