In the bowl of a food processor, add all of the ingredients and purée until smooth. Using a rubber spatula, scrape down the sides of the bowl and check for any chunks of peach. Purée again until completely smooth. Strain the mixture through a fine-mesh sieve set over a large bowl, pressing on the solids. Cover the strained mixture with plastic wrap and refrigerate until completely chilled, preferably overnight. Once chilled, place half the mixture into the bowl of an ice cream maker and freeze according to the manufacturer's directions. Transfer the sherbet to a freezer-safe container and freeze until firm. Repeat with the remaining peach mixture, making sure the ice cream bowl is frozen before using. Enjoy!