Make blueberry sauce: In a wide, shallow pan, combine blueberries, sugar, cardamom, and water. Heat over medium flame for 5 minutes until berries soften and burst. Mash with potato masher. Continue cooking 5-10 minutes until thick and jammy. Cool 15 minutes.
Prepare base: In large bowl, combine cold milk and cream. Stir in cooled blueberry sauce. Refrigerate 1+ hours until completely cold.
Stir mixture well (it may have separated). Pour into ice cream maker, filling no more than 2/3 full. Churn according to manufacturer's instructions, about 20-25 minutes.
Transfer to freezer-safe container. Cover and freeze 8 hours until solid.