This started as an experiment with a custard-style ice cream base and has become a requested favorite for get-togethers. The sweetness of the peach and smooth cream gets a boost from the earthy spices without being overpowering. I eat it plain but a few friends enjoy it in ice cream sandwiches.
Whisk milk, sugar, and salt together in a saucepan over medium heat; bring to a simmer. Stir peach puree, ginger, cinnamon, and vanilla extract; simmer until flavors blend, 5 to 10 minutes.
Place egg yolks in a small bowl. Slowly pour 1/2 cup hot milk mixture into eggs, whisking constantly. Pour warmed egg mixture into the milk mixture in the saucepan over medium heat. Cook, stirring occasionally, until thick, 5 to 10 minutes. Strain egg mixture into a chilled bowl and refrigerate, stirring occasionally, until chilled, about 2 hours.
Whisk cream into chilled egg mixture; add peaches and stir.
Pour peach mixture into the container of an ice cream maker and freeze according to the manufacturer's instructions.
Tempering the eggs and straining the mix will help reduce any egg bits from cropping up and give a smoother texture for the finished custard ice cream.