Whisk together the egg yolks and sugar in a large heavy saucepan. Whisk in the milks. Cook over medium-low, stirring constantly, 15 minutes or until the mixture coats the back of a spoon. Stir in the peaches and vanilla.

Cool completely (about 30 minutes); cover and chill at least 4 hours or up to 8 hours.

Pour the custard into the freezer container of a 2 1/2 to 3-quart electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and times may vary.) Transfer to a freezer-safe container; freeze 2 hours or until firm.