Whisk together the sugar, water, corn syrup and cocoa powder in a medium saucepan over medium heat until the mixture begins to bubble at the edges. Cook for about 1 minute, whisking the entire time. Remove from the heat, stir in the vanilla and let cool. Chill in the refrigerator for at least 2 hours before using. It can be stored for up to 2 weeks, covered, in the refrigerator.
To make the frozen yogurt, freeze the vanilla yogurt in your ice cream maker according to manufacturer's instructions. Once frozen, fold in graham crackers and marshmallows.
In a freezer-safe container, make a thin layer of frozen yogurt, drizzle with fudge swirl, and repeat until all the frozen yogurt is in the container. Freezer overnight before serving.