Preheat oven to 375 degrees F. Put the peaches and blackberries on a baking sheet and roast, turning once, until very soft and caramelized, about 30 minutes. Remove to a plate and let cool. The fruit can be roasted a day ahead of time and stored in a container with a tight-fitting lid for up to 1 day.
Combine the fruit, yogurt, peach nectar, vanilla and 1 cup ice cubes in a blender and blend until smooth. Divide among 2 large glasses.