Gently toss raspberries with granulated sugar and 1 teaspoon of the vanilla in small bowl. Set aside until ready to serve.
Mix butter, brown sugar, ginger and remaining 1/2 teaspoon vanilla in large bowl. Add peach halves; toss gently to coat well.
Fold the edges of a sheet of heavy duty foil to form a shallow baking pan. Place on grill over medium heat. Arrange peaches, cut-side down, on foil. Cover with second sheet of foil.
Grill 6 to 8 minutes or until browned and caramelized around edges, turning once. To serve, place 2 peach halves on each dessert plate. Top with ice cream and raspberry mixture. Serve immediately.