Cut three of the peeled, pitted peaches into large chunks and place them in the bowl of a food processor with 3/4 cup sugar. Pulse until completely smooth. Add Greek yogurt and vanilla. Pulse again until well combined. Transfer the yogurt mixture to an ice cream maker and freeze according to manufacturer's directions.
Meanwhile, dice the remaining peach and add to yogurt as it's processing, about 5 minutes before the end of the recommended freezing time. Serve immediately or transfer to an airtight freezer-safe container and freeze.
Yields appoximately 1 quart.
Frozen yogurt will be soft-serve consistency if served immediately after processing. If frozen, it will firm up more. To soften, allow to sit out for 10 to 15 minutes before scooping and serving.