1. Combine raspberries and lemon juice in food processor fitted with metal blade; process until smooth. Refrigerate until ready to serve.
2. Prepared grill for direct cooking.
3. Combine brown sugar, cinnamon and rum, if desired, in medium bowl; coat peach halves with mixture. Place peach halves, cut sides up, on large sheet foil. Dot with butter. Fold foil over peaches, leaving head space for steam; seal foil. Place packet on grid over medium heat. Grill 15 minutes. Remove from grill; carefully open end of packet to allow steam to escape.
4. To serve, spoon 2 tablespoons raspberry sauce over each peach half. Garnish with fresh mint sprig.
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