In a large bowl, whisk together the egg yolks and sugar.
In a large saucepan, bring the cream and milk to a simmer over low heat. Whisking constantly, slowly pour the hot milk mixture into the egg mixture until combined; return the combined mixture to the saucepan. Cook over low heat for 3 to 5 minutes or until the custard has thickened enough to coat the back of the spoon, stirring constantly. Immediately strain the custard into a bowl. Set the bowl in a larger bowl filled with ice water to cool, stirring occasionally.
Stir the lemon juice and vanilla into the cooled custard. Freeze in an ice cream maker according to the manufacturer's instructions, adding the peach chunks halfway through the churning process.