In a large mixing bowl, combine chopped peaches, grated ginger, 1/2 cup sugar, salt, and lemon juice. Cover and let macerate for 30 minutes.
While the peaches are macerating, whisk together egg yolks until light in color. Add the remaining 1/2 cup sugar and whisk until combined.
In a small saucepan, warm heavy cream and milk over medium heat. Just to a slight simmer, stirring occasionally.
Temper the eggs by slowly drizzling the hot cream mixture into the eggs, whisking vigorously the entire time, until about 1/3 of the cream has been added. Transfer the egg mixture into the saucepan and heat on low until the mixture thickens enough to coat the back of a spoon. Remove from heat and stir in vanilla and the peaches with all the juices that they've released.
Let cool to room temperature and then refrigerate for at least 8 hours, or until chilled.
Freeze in an ice cream maker according to the machine's instructions. Once done, fold in the chopped gingersnaps and transfer to freezer-safe container.
Freeze overnight for the best consistency.