Mix wine, oil, sage, smoked paprika, garlic salt and pepper in large bowl. Add mushrooms; toss to coat well. Cover. Refrigerate 15 minutes or longer for extra flavor.
Grill mushrooms in grilling basket over medium-high heat 10 minutes or until tender and well browned, stirring occasionally. Grill bread slices 1 to 2 minutes per side or until grill marks appear.
Arrange bread slices in single layer on large perforated grilling tray or disposable aluminum grilling tray. Layer evenly with 1 1/2 cups of the cheese and grilled mushrooms. Sprinkle with remaining 1/2 cup cheese. Place tray on grill. Grill over medium-high heat with lid closed 2 minutes or until cheese is melted. Sprinkle toasts with parsley and drizzle with balsamic glaze. Serve immediately.