Add the yogurt, cocoa powder, vanilla, and sweetener to your food processor. Process until completely smooth, stopping once to scrape the sides and bottom of the bowl. Taste and decide if you'd like to add more sweetener.
Using a spatula, transfer the mixture to a square 9-inch pan. Cover with cling wrap and freeze for one hour.
Remove the pan from the freezer. Use a fork to stir the already-frozen edges into the still-soft center. If the edges are very frozen, you might need to scrape them with a knife. Stir the mixture until smooth, then spread it evenly in the pan.
Cover the pan again, and place it in the freezer for 3 more hours, repeating the process of stirring the yogurt every 60 minutes.
When the entire mixture is frozen, serve immediately as soft-serve yogurt (use chilled bowls), or freeze for two more hours for a firmer consistency that you can scoop out with an ice cream scoop. If frozen overnight, remove the yogurt from the freezer 10 minutes before serving to allow it to soften.
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Notes
The nutrition info assumes that a sugar-free sweetener was used. You can use ½ cup of any granulated sweetener instead of stevia, but a powdered sweetener is best. You can also use ½ cup of honey.
I highly recommend using whole-milk yogurt. This will give you the best flavor and texture.
Please use Greek yogurt. Regular yogurt is too liquid and won't work in this recipe.
Stirring prevents large ice crystals from forming and helps achieve a creamy consistency.
I recommend using Dutch-processed cocoa powder in this recipe. Dutch processing adds an alkali to the cacao, reducing its acidity. Natural cacao powder is quite acidic. Dutch-processed cocoa powder is milder.
You can keep this yogurt in the freezer for up to three months. The longer you keep it, the icier it will become, so remove it from the freezer 30 minutes before serving it. Sometimes, if it's been in the freezer for a while, I run it through the food processor to remove the iciness and make a creamy soft-serve froyo.