Freeze ice cream maker freezer bowl at least 24 hours. It's important that it's very, very cold for the best ice cream consistency.
Put half the blueberries ( 1 cup) and water in small saucepan over low heat. Cover and cook for 10 minutes, stirring frequently.
Place in blender along with remaining blueberries. Puree. Add sugar, lemon zest and salt. Blend a minute or so. Scrape mixture into a bowl. Cover; place in freezer to chill at least 30 minutes. You want it nice and cold when it goes into the ice cream maker.
Whisk in cream and half and half. Add to ice cream maker. Follow manufacturer's directions to churn ice cream. In about 20-30 minutes, the ice cream will reach a creamy soft-serve consistency. Just before finishing churning, add the graham cracker pieces and let them mix in.
For a firmer consistency, remove from freezer bowl and place in freezer for several hours. Store in sealed container.