Optional for extra creaminess: Place a mesh colander lined with a paper towel over a bowl. Add yogurt and let strain for 1-2 hours. Discard liquid and proceed with the recipe.
Stir together all ingredients until well combined. Taste to adjust the sweetness as you like.
Place in a freezer-safe container, seal the lid, and freeze for 3-4 hours (until just firm) and stir vigorously to break up any parts of the frozen yogurt that have frozen more solid than others. Serve.
(Or freeze overnight and let sit at room temperature for a bit before serving so it's very creamy (and not frozen solid). Stir and mash it up before serving for the creamiest consistency and to break up any ice crystals that form. You can also microwave it for 30-60 seconds, then stir, to serve more quickly from the freezer.)
Notes
Freeze in individual portions if desired for up to 3 months. Smaller portions will soften faster at room temperature.
Let sit at room temperature for a bit before serving so it's very creamy (and not frozen solid).
Try adding 1 cup minced strawberries, raspberries, or peaches.
You could churn this in an ice cream maker and serve immediately for a soft frozen texture.
To make this with regular yogurt, simply place a little more than the recipe calls for into a paper towel-lined fine-mesh sieve placed over a bowl. Let it drain for at least an hour (or longer) to remove some of the liquid and thicken the yogurt.
Dairy-free: Try coconut cream (from a can) or nondairy Greek style yogurt like the kind from Siggi's.