Heat grill to medium. Halve and pit peaches; prick skins with a fork. In a bowl, stir together butter and light-brown sugar; brush butter mixture over peach halves, coating entirely.
Make the raspberry sauce: In a bowl, toss raspberries with sugar; let sit 5 minutes. Pass through a sieve into another bowl, pressing with a spoon to extract as much liquid as possible; discard solids.
Grill peaches on both sides until fruit is tender, 5 to 10 minutes. Serve warm, topped with ice cream and drizzled with raspberry sauce.