Place mushrooms on grill over medium heat. Cover grill; cook 8 to 10 minutes, turning once, until tender. Add bread slices to grill for last 2 minutes of cooking time, turning once, until toasted. Cut mushrooms into 1/4-inch-thick slices. Spread goat cheese on 1 side of each bread slice. Top with mushroom and pepper slices. Sprinkle with basil. Drizzle with balsamic glaze.