Add the Greek yogurt, honey or maple syrup, and vanilla extract to a food processor or blender. Blend until completely smooth.

If making the berry version, mash the berries with a fork until no large chunks remain. If using frozen berries, let them thaw slightly first. Stir in the chia seeds and let the mixture sit for 10 minutes to thicken.

Transfer half of the yogurt mixture to a freezer-safe container. Spoon the berry mixture over the top and gently swirl with a spoon. Top with the remaining yogurt mixture.

Freeze for about 4 hours.

Let the frozen yogurt sit at room temperature for about 15 minutes before scooping and serving. If frozen overnight or longer, it may need a few extra minutes to soften.