Combine the brown sugar, lime juice, and vinegar in a small saucepan and simmer for 10 minutes to thicken slightly. Remove from the heat, allow to cool, add the peaches, and marinate for an additional 20 minutes.
To make the puree, slightly thaw the raspberries. Place all the ingredients in a blender or food processor and puree until smooth.
Grilling and Assembly
Remove the peaches from the marinade and place them in a grill basket with handles. Grill them flesh side down over a medium-hot fire. Grill for 2 to 3 minutes until the grill marks show. Turn and grill until the peaches are soft.
To serve, spoon some of the raspberry puree on a dessert plate, place the peach cut side up on the sauce. Put a dollop of cheese in the center of the peach and top with additional puree, and garnish with the walnuts.