Whisk eggs and brown sugar together in a large bowl.

Heat milk and heavy cream in a saucepan over low heat and bring to a simmer.

Slowly add the milk mixture to the egg mixture, whisking constantly.

Return to the saucepan and cook for 3-5 minutes, stirring constantly, until slightly thickened.

Strain custard through a sieve into a large bowl.

Stir in lemon juice and vanilla.

Cool custard in an ice water bath or refrigerate overnight.

Chop peaches and sprinkle a couple teaspoons of sugar over them to macerate. Refrigerate until ready to use.

Freeze custard in ice cream maker (according to manufactures' instructions)

Add peaches to the custard about half-way through the churning process.

Transfer to a container and store in freezer.