Preheat oven to 375°.
Place matzo crackers in a single layer on a baking sheet; bake at 375° for 5 minutes or until lightly browned. Break crackers into small pieces, and place in a large bowl. Pour chicken broth and water over matzo; let stand 10 minutes, stirring occasionally.
Heat oil in a large nonstick skillet over medium heat. Add onion; cover and cook 5 minutes, stirring occasionally. Add carrot and next 6 ingredients (carrot through mushrooms) to pan; cover and cook 5 minutes or until onion is tender. Add mushroom mixture and 2 tablespoons parsley to matzo mixture, stirring well. Combine egg whites and eggs in a bowl; stir with a whisk. Add egg mixture to matzo mixture; stir well.
Press matzo mixture into a 10-inch deep-dish pie plate coated with cooking spray. Bake, covered, at 375° for 20 minutes. Uncover and bake an additional 18 minutes or until lightly browned. Let kugel stand for 5 minutes, and cut into wedges. Garnish with parsley sprigs, if desired.