Freeze ice cream bowl for 24 hours.
Combine blueberries and sugar in a medium sized saucepan over medium heat. Do not cover but mashed blueberries with spatula and stir until sugar dissolves, about 5 minutes.
Removed from heat and pour into a large bowl. Stir in half-and-half and cream. Cover and refrigerate for at least 2 hours.
Place frozen bowl on base of ice cream maker and turn it on. Pour chilled mixture into frozen bowl and churn until desired consistency, about 15 to 20 minutes.
If you prefer a firmer consistency, transfer ice cream to a container and place in freezer for a couple of hours.