Combine rhubarb, 1/2 cup water and sugar in heavy large saucepan. Scrape in seeds from vanilla bean; add bean. Cook over medium heat until rhubarb is almost tender, stirring occasionally, about 7 minutes. Add strawberries and cook 3 minutes. Transfer to bowl. Refrigerate until cold, about 4 hours.
Mix yogurt and vanilla extract in medium bowl. (Strawberry-rhubarb mixture and vanilla yogurt can be prepared 2 days ahead. Cover separately and chill.)
In each of 8 wineglasses or goblets, layer scant 1/4 cup yogurt mixture, 1/2 teaspoon golden brown sugar and 1/4 cup strawberry-rhubarb mixture. Repeat layering. (Parfaits can be prepared 4 hours ahead. Cover and refrigerate.)
