Place peaches and water in a large skillet; cook, uncovered, over medium heat until tender. Place in a food processor; cover and process until blended. Set aside.
In a small saucepan, heat milk to 175°; stir in sugar until dissolved. Whisk a small amount of the hot mixture into egg yolks. Return all to the pan, whisking constantly. Cook over low heat until mixture is just thick enough to coat a metal spoon and a thermometer reads at least 160°, stirring constantly. Do not allow to boil. Remove from heat immediately.
Quickly transfer to a large bowl; place bowl in a pan of ice water. Stir gently and occasionally for 2 minutes. Stir in cream, peaches and liqueur if desired. Press plastic wrap onto surface of custard. Refrigerate several hours or overnight.
Fill cylinder of ice cream freezer two-thirds full; freeze according to the manufacturer’s directions. (Refrigerate any remaining mixture until ready to freeze.) Transfer ice cream to freezer containers, allowing headspace for expansion. Freeze 2-4 hours or until firm. Repeat with any remaining gelato mixture.