If using fresh peaches, score an X on the bottom, blanch in boiling water for 30-60 seconds, then transfer to an ice bath. Peel, pit, and chop into 1-inch pieces.
Combine the prepared peaches, sugar (or honey), and lemon juice in a blender. Blend on high until completely smooth, about 30-60 seconds.
Pour the peach puree into a large bowl. Stir in the Greek yogurt, vanilla extract, and cinnamon (if using) until fully combined and uniform in color.
Cover the mixture and refrigerate for at least 1 hour, or up to overnight. The colder the base, the creamier the final texture.
Set up your ice cream maker with the frozen bowl and turn it on. Pour the chilled peach yogurt mixture through the opening and churn for 20-25 minutes until it reaches a thick, soft-serve consistency.
Transfer the churned frozen yogurt to an airtight container. Press plastic wrap directly onto the surface, seal with the lid, and freeze for at least 2-4 hours or overnight until firm.
Let the frozen yogurt sit at room temperature for 5-10 minutes before scooping. Run your scoop under hot water for clean, round scoops. Serve and enjoy.