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.