Combine the raspberries, sugar, and lemon juice in a blender and puree. Strain through a fine mesh strainer. Can be made 2 days ahead. Store covered in the refrigerator until ready to serve.

Prepare the grill for direct heat and preheat to medium-high.

Cut the peaches in half and remove the pits.

Combine the butter and sugar in a small bowl. Brush the sugar mixture thickly on the cut sides of the peaches.

Brush the grill grates with oil. Grill the peaches, cut side down, for 5-6 minutes or until nicely marked and just starting to soften.

Place a little raspberry sauce on the bottom of each serving plate, top with a peach half, a scoop of ice cream, more raspberry sauce, and a mint sprig. Serve immediately.