Place the raspberries, yogurt, sweetener, and vanilla in your food processor bowl. Process until smooth, stopping a few times to scrape the sides and bottom of the bowl. A few specks of raspberries will remain – that’s fine.
Using a spatula, transfer the mixture to a glass square 8-inch pan (or a similar-capacity glass pan). Cover with cling wrap and freeze for 45 minutes.
Remove the pan from the freezer. Use a spatula to stir the already-frozen edges into the still-soft center, then use a hand whisk to mix everything together until smooth.
Cover the pan again and place it in the freezer for 2 more hours, repeating the process of stirring the yogurt every 30 minutes.
When the entire mixture is frozen, serve immediately as soft-serve yogurt (use chilled bowls), or freeze for 1-2 more hours for a firmer consistency you can scoop out.
Video
Notes
It's important to use a strained yogurt in this recipe - either Greek yogurt or Skyr. It's also important to use whole-milk yogurt (not low-fat or nonfat).
I made several attempts before perfecting this recipe, playing with the amount of sweetener used. Since the yogurt and raspberries are fairly tart, this dessert requires a fair amount of sweetener. So, to keep carbs and sugar in check, I use stevia glycerite, a formulation that greatly reduces the aftertaste typical of stevia products. But you can use a granulated sweetener or honey instead.
You can keep this yogurt in an airtight freezer-safe container in the freezer for up to three months. It hardens as it sits in the freezer, so make sure to remove it from the freezer 30 minutes before you serve it.