In a small saucepan, bring the sugar and water to a boil over medium-high heat. Simmer, stirring occasionally, until the sugar has dissolved, about 5 minutes. Cool for 20 minutes.
Pour the cooled syrup into a blender. Add the yogurt, raspberries, apple juice, vanilla, and ice. Blend until the mixture is smooth and thick.
Pour into glasses and serve.
Recipe courtesy Giada De Laurentiis