In a bowl, combine the chopped peaches, 1/2 cup sugar, lemon juice, and peach brandy. Cover and refrigerate for 2 ~ 3 hours or overnight. Remove the peach mixture from the refrigerator and drain the juice into a cup. Set aside and return the peaches to the refrigerator.
In a medium saucepan, combine 3/4 cup granulated sugar, the heavy cream, milk, and vanilla. Bring just to a boil. Be careful that the mixture does not boil over.
In a medium bowl, whisk the egg yolks. While whisking, stream in about 1/3 cup of the boiled cream mixture. While whisking the cream/milk/egg mixture, return it to the remaining cream/milk mixture and continue stirring. The mixture will thicken as it returns to a boil.
Remove the mixture from the heat. Strain into a stainless bowl. Stir in the reserved peach juice. Set the bowl over a larger bowl filled with ice.
Once the custard mixture is cool, cover and place it in the refrigerator until the custard is very cold, for several hours or overnight.
Transfer the custard to the ice cream maker and freeze according to the manufacturer's instructions. After the ice cream begins to stiffen, when very close to done, add the peaches and continue to freeze until done.
Remove ice cream to a container and set in the freezer until ready to serve.