Place the yogurt, honey and vanilla in your food processor’s bowl.
Process to incorporate, stopping once to scrape the sides of the bowl, then process 1 more minute, until light and fluffy. You can also whisk by hand, but do so for several minutes until smooth and fluffy.
Using a spatula, transfer the mixture to a square 9-inch glass 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 1-2 more hours for a firmer consistency that you can scoop out with an ice cream scoop.
If you end up storing the frozen yogurt for longer than that (say, overnight or a couple of days - I doubt it will last longer), remove it from the freezer 30 minutes before serving, to allow it to soften.
*To keep this homemade frozen yogurt low carb, you can use a low carb honey or maple syrup, Swerve Confectioners, or stevia. 1/2 cup of the low carb version has 114 calories and 4 grams of carbs.