To make ice cream: In a blender, combine one of the peaches, datil peppers and 2 cups of half and half. Blend on high until completely pureed. In a saucepan, combine the puree with remaining half and half, heavy cream, vanilla, sugar and sea salt. Simmer on medium-low heat, whisking frequently, until mixture reaches 175°. (Don’t go above 185°.) Remove from heat and whisk in peach preserves. Chill mixture. Cut remaining peach in half and slice into very thin slivers. Once the mixture is chilled, whisk in chopped ginger and fresh peach pieces. Churn until smooth according to ice cream freezer instructions.
To make cookies: Preheat oven to 325°. In large bowl, combine butter and sugars. Cream until smooth. Beat in one egg at a time, scraping down the sides periodically. Continue creaming until light and fluffy. In a separate bowl, combine all dry ingredients and whisk until everything is incorporated. Add the dry ingredients to butter mixture and blend together. Before dough comes together, add chocolate chips and mix until blended. Scoop dough to desired size and roll in cinnamon sugar. Bake for 8 minutes, rotate cookie sheets and bake for 8 more minutes. Cool on a wire rack.
To assemble: Soften ice cream slightly. Spoon a generous amount of ice cream on flat side of one cookie. Top with flat side of another cookie and gently press down. Freeze 15 minutes before eating.