Place the yogurt, honey, and vanilla in your food processor’s bowl or in a medium mixing bowl.
Process the ingredients to incorporate, stopping once to scrape the sides of the bowl, then process for 1 more minute until light and fluffy. If mixing by hand, mix for 2-3 minutes until smooth and fluffy.
Using a spatula, transfer the mixture to a square 9-inch glass or ceramic baking dish. Cover with cling wrap and freeze for 45 minutes.
Remove the pan from the freezer. Use a rubber spatula to stir the already-frozen edges into the still-soft center, then spread evenly again.
Cover again, and place 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 a soft-serve yogurt (use chilled bowls), or freeze it for 1-2 more hours for a firmer consistency that you can scoop out with an ice cream scoop.
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Notes
To keep this yogurt low-carb, you can use a sugar-free sweetener.
While regular yogurt is delicious, you should definitely use Greek yogurt in this recipe.
Use high-quality pure vanilla extract for the best results.
You can keep this yogurt in a sealed container in the freezer for up to a month. But the longer it stays in the freezer, the less creamy and icier it will become. If it's spent longer than a day in your freezer, remove it from the freezer about 30 minutes before enjoying it.