Combine yogurt, cream, sugar, and vanilla extract together until the sugar has dissolved.
Transfer mixture to a large freezer bag.
Remove all air from the bag prior to sealing.
Lay bag flat in the freezer.
After ~1 hour, take it out and smoosh it around. Lay it flat in the freezer again.
Repeat this process every hour. As yogurt freezes, break up all the chunks each time you take it out. Try laying the bag flat on a counter and use your fingers to push through any lumps.
When it is well frozen and smooth, it is ready.
Serve immediately.
Notes
Try honey or other sweeteners for a change from plain sugar.