1. Light grill. Place mushroom caps on large baking sheet. Mix 3 1/2 tablespoons of the oil, rosemary, and salt and pepper to taste in small bowl. Brush oil mixture over both sides of mushrooms.
2. Grill mushrooms, gill side up over medium-hot fire, until caps are cooked through and grill-marked, 8 to 10 minutes.
3. Meanwhile, grill bread until golden brown on both sides. Place toast slices on large platter. Rub garlic over tops, then brush with remaining 2 1/2 tablespoons oil.
4. Halve grilled mushrooms; place one half, gill side down, over each slice of toast. Serve immediately.